Seach the website
Login
Register
Dark Mode
Brightness
Profile
Edit Profile
Messages
My favorites
My Updates
Logout
Learn more about SANRAL Bursaries
Home
Tag
integer
Recent questions tagged integer
109
views
1
answers
Prove the mean value theorem by first reducing to the case \( u(a)=u(b)=0 \) and then using the fact that \( u(x) \) must take on a maximum or minimum value for some point \( \bar{x} \) in \( (a, b) \).
Prove the mean value theorem by first reducing to the case \( u(a)=u(b)=0 \) and then using the fact that \( u(x) \) must take on a maximum or minimum value for some poin...
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 16
Mathematics
function
prove
theorem
positive
bounded
integer
taylor
+
–
75
views
2
answers
Find a linear differential equation with constant coefficients satisfied by \( e^{2 x}, e^{-x}, e^{3 x} \), and \( e^{5 x} \).
Find a linear differential equation with constant coefficients satisfied by \( e^{2 x}, e^{-x}, e^{3 x} \), and \( e^{5 x} \).
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 7
Mathematics
function
coefficients
positive
integer
equation
differential
solution
+
–
68
views
2
answers
Find a linear differential equation with constant coefficients satisfied by \( e^{-2 x} \) and \( e^{x} \cos 2 x \).
Find a linear differential equation with constant coefficients satisfied by \( e^{-2 x} \) and \( e^{x} \cos 2 x \).
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 7
Mathematics
differential
function
equation
positive
coefficients
integer
solution
+
–
552
views
1
answers
What is the power rule for differentiation?
What is the power rule for differentiation?
Maths-Genie
Bronze Status
9.4k
points
Maths-Genie
asked
Apr 19, 2023
Mathematics
rule
state
differentiation
exponents
integer
+
–
639
views
1
answers
What is an integer?
What is an integer?
AstraNova
Diamond
67.9k
points
AstraNova
asked
Feb 6, 2023
Mathematics
function
numbers
equations
integer
positive
prove
algebra
+
–
507
views
1
answers
What is a whole number?
What is a whole number?
AstraNova
Diamond
67.9k
points
AstraNova
asked
Feb 6, 2023
Mathematics
number
whole
natural
numbers
integer
real
remainder
+
–
384
views
0
answers
Calculate the sum of the digits of \(2^{2015} \times 5^{2019}\)
Calculate the sum of the digits of \(2^{2015} \times 5^{2019}\)
AstraNova
Diamond
67.9k
points
AstraNova
asked
Jan 30, 2023
Mathematics
calculate
digits
numbers
question
integer
triangle
+
–
363
views
1
answers
Prove that any polynomial of degree n has at most n roots.
Prove that any polynomial of degree n has at most n roots.
AstraNova
Diamond
67.9k
points
AstraNova
asked
Jan 27, 2023
Mathematics
function
prove
integer
theorem
bounded
taylor
positive
+
–
219
views
0
answers
Let \(f(x)\) be the polynomial \(\prod_{k=1}^{50}(x-(2 k-1))\). Let \(c\) be the coefficient of \(x^{48}\) in \(f(x)\). When \(c\) is divided by 101 , what is the remainder? (The remainder is an integer between 0 and 100.)
Let \(f(x)\) be the polynomial \(\prod_{k=1}^{50}(x-(2 k-1))\). Let \(c\) be the coefficient of \(x^{48}\) in \(f(x)\). When \(c\) is divided by 101 , what is the remaind...
MathsGee
Platinum
113k
points
MathsGee
asked
Dec 8, 2022
Mathematics
function
integer
product
written
digit
expression
+
–
278
views
0
answers
A mustache is created by taking the set of points \((x, y)\) in the \(x y\) coordinate plane that satisfy \(4+4 \cos (\pi x / 24) \leq y \leq 6+6 \cos (\pi x / 24)\) and \(-24 \leq x \leq 24\). What is the area of the mustache?
A mustache is created by taking the set of points \((x, y)\) in the \(x y\) coordinate plane that satisfy \(4+4 \cos (\pi x / 24) \leq y \leq 6+6 \cos (\pi x / 24)\) and ...
MathsGee
Platinum
113k
points
MathsGee
asked
Dec 8, 2022
Mathematics
points
prove
integer
coordinates
line
parallel
theorem
+
–
274
views
0
answers
What remainder do you get when you divide \(n\) by 100 ? (The remainder is an integer between 0 and 99, inclusive.)
Consider the base 27 number\[n=A B C D E F G H I J K L M N O P Q R S T U V W X Y Z,\]where each letter has the value of its position in the alphabet. What remainder do yo...
MathsGee
Platinum
113k
points
MathsGee
asked
Dec 8, 2022
Mathematics
integer
product
expression
digit
written
function
positive
+
–
271
views
0
answers
For each integer from 1 through 2019, Tala calculated the product of its digits. Compute the sum of all 2019 of Tala's products.
For each integer from 1 through 2019, Tala calculated the product of its digits. Compute the sum of all 2019 of Tala's products.
MathsGee
Platinum
113k
points
MathsGee
asked
Dec 8, 2022
Mathematics
integer
triangle
pascal
row
pattern
numbers
question
+
–
341
views
0
answers
In the USA, standard letter-size paper is \(8.5\) inches wide and 11 inches long. What is the largest integer that cannot be written as a sum of a whole number (possibly zero) of 8.5's and a whole number (possibly zero) of 11's?
In the USA, standard letter-size paper is \(8.5\) inches wide and 11 inches long. What is the largest integer that cannot be written as a sum of a whole number (possibly ...
MathsGee
Platinum
113k
points
MathsGee
asked
Dec 8, 2022
Mathematics
numbers
integer
remainder
multiple
divisor
real
matrix
+
–
563
views
1
answers
Let \(G\) be the set of points \((x, y)\) such that \(x\) and \(y\) are positive integers less than or equal to 6 .
Let \(G\) be the set of points \((x, y)\) such that \(x\) and \(y\) are positive integers less than or equal to 6 . A magic grid is an assignment of an integer to each po...
MathsGee
Platinum
113k
points
MathsGee
asked
Dec 8, 2022
Mathematics
integer
positive
grid
assignment
function
integers
+
–
400
views
0
answers
The number \(734,851,474,594,578,436,096\) is equal to \(n^6\) for some positive integer \(n\). What is the value of \(n\) ?
The number \(734,851,474,594,578,436,096\) is equal to \(n^6\) for some positive integer \(n\). What is the value of \(n\) ?
MathsGee
Platinum
113k
points
MathsGee
asked
Dec 8, 2022
Mathematics
positive
integer
number
multiple
values
toys
cars
+
–
414
views
0
answers
Let \(S\) be the set of numbers of the form \(n^5-5 n^3+4 n\), where \(n\) is an integer that is not a multiple of 3 . What is the largest integer that is a divisor of every number in \(S\) ?
Let \(S\) be the set of numbers of the form \(n^5-5 n^3+4 n\), where \(n\) is an integer that is not a multiple of 3 . What is the largest integer that is a divisor of ev...
MathsGee
Platinum
113k
points
MathsGee
asked
Dec 8, 2022
Mathematics
numbers
integer
multiple
divisor
remainder
+
–
267
views
0
answers
Determine the largest integer \(n\) such that \(n<103\) and \(n^3-1\) is divisible by 103 .
Determine the largest integer \(n\) such that \(n<103\) and \(n^3-1\) is divisible by 103 .
MathsGee
Platinum
113k
points
MathsGee
asked
Dec 8, 2022
Mathematics
numbers
question
divisible
integer
largest
value
remainder
+
–
199
views
0
answers
If \(\mathrm{A}\) and \(\mathrm{B}\) are subset \(\mathrm{s}\) of \(\mathrm{X}=\{1,2,3,4,5\}\) then find the probability such that \(\mathrm{n}(\mathrm{A} \cap \mathrm{B})=2\).
If \(\mathrm{A}\) and \(\mathrm{B}\) are subset \(\mathrm{s}\) of \(\mathrm{X}=\{1,2,3,4,5\}\) then find the probability such that \(\mathrm{n}(\mathrm{A} \cap \mathrm{B}...
Maths-Genie
Bronze Status
9.4k
points
Maths-Genie
asked
Nov 29, 2022
Mathematics
function
prove
bounded
positive
theorem
integer
taylor
+
–
241
views
0
answers
If \(\mathrm{p}(\mathrm{x})\) be a polynomial of degree three that has a local maximum value 8 at \(\mathrm{x}=1\) and a local minimum value 4 at \(\mathrm{x}=2\); then \(\mathrm{p}(0)\) is equal to
If \(\mathrm{p}(\mathrm{x})\) be a polynomial of degree three that has a local maximum value 8 at \(\mathrm{x}=1\) and a local minimum value 4 at \(\mathrm{x}=2\); then \...
Maths-Genie
Bronze Status
9.4k
points
Maths-Genie
asked
Nov 29, 2022
Mathematics
function
integer
bounded
theorem
prove
positive
taylor
+
–
202
views
0
answers
Let \(\alpha\) and \(\beta\) be the roots of the equation, \(5 \mathrm{x}^2+6 \mathrm{x}-2=0\). If \(\mathrm{S}_{\mathrm{n}}=\alpha^{\mathrm{n}}+\beta^{\mathrm{n}}, \mathrm{n}=1,2,3, \ldots .\). , then :
Let \(\alpha\) and \(\beta\) be the roots of the equation, \(5 \mathrm{x}^2+6 \mathrm{x}-2=0\). If \(\mathrm{S}_{\mathrm{n}}=\alpha^{\mathrm{n}}+\beta^{\mathrm{n}}, \math...
Maths-Genie
Bronze Status
9.4k
points
Maths-Genie
asked
Nov 29, 2022
Mathematics
positive
prove
function
integer
theorem
taylor
bounded
+
–
587
views
0
answers
Let \(\alpha>0, \beta>0\) be such that \(\alpha^3+\beta^2=4\). If the maximum value of the term independent of \(x\) in the binomial expansion of \(\left(\alpha x^{1 / 9}+\beta x^{-1 / 6}\right)^{10}\) is \(10 k\), then \(k\) is equal to :
Let \(\alpha>0, \beta>0\) be such that \(\alpha^3+\beta^2=4\). If the maximum value of the term independent of \(x\) in the binomial expansion of \(\left(\alpha x^{1 / 9}...
Maths-Genie
Bronze Status
9.4k
points
Maths-Genie
asked
Nov 29, 2022
Mathematics
function
taylor
positive
prove
theorem
bounded
integer
+
–
760
views
1
answers
Find all monic polynomials \(p(x)\) with integer coefficients of degree two for which there exists a polynomial \(q(x)\) with integer coefficients such that \(p(x) q(x)\) is a polynomial having all coefficients \(\pm 1\).
Find all monic polynomials \(p(x)\) with integer coefficients of degree two for which there exists a polynomial \(q(x)\) with integer coefficients such that \(p(x) q(x)\)...
MathsGee
Platinum
113k
points
MathsGee
asked
Sep 23, 2022
Mathematics
monotonic
polynomials
integer
coefficients
+
–
618
views
0
answers
For an integer \(n \geq 2\), let \(D_n\) be the set of points \((x, y)\) of the plane with integer coordinates such that \(-n \leq x, y \leq n\).
For an integer \(n \geq 2\), let \(D_n\) be the set of points \((x, y)\) of the plane with integer coordinates such that \(-n \leq x, y \leq n\).(a) Each of the points of...
MathsGee
Platinum
113k
points
MathsGee
asked
Sep 23, 2022
Mathematics
integer
points
coordinates
prove
+
–
223
views
0
answers
A natural number \(n\) is called sensible if there is an integer \(r\) with \(1<r<n-1\) such that the representation of \(n\) in base \(r\) has all the digits equal.
A natural number \(n\) is called sensible if there is an integer \(r\) with \(1<r<n-1\) such that the representation of \(n\) in base \(r\) has all the digits equal. For ...
MathsGee
Platinum
113k
points
MathsGee
asked
Sep 23, 2022
Mathematics
natural
number
sensible
integer
digits
equal
+
–
215
views
0
answers
A function \(f\) is defined on the set \(\mathbb{N}\) and satisfies
A function \(f\) is defined on the set \(\mathbb{N}\) and satisfies(i) \(f(1)=1\),(ii) \(f(2 n+1)=f(2 n)+1\),(iii) \(f(2 n)=3 f(n)\)for all \(n \in \mathbb{N}\). Find the...
MathsGee
Platinum
113k
points
MathsGee
asked
Sep 23, 2022
Mathematics
function
value
bounded
theorem
positive
integer
taylor
+
–
604
views
0
answers
Let \(A\) be the set of cubic polynomials \(f(x)\) with the leading coefficient 1 having the following property:
Let \(A\) be the set of cubic polynomials \(f(x)\) with the leading coefficient 1 having the following property: There exist a prime number \(p\) not dividing 2004 and a ...
MathsGee
Platinum
113k
points
MathsGee
asked
Sep 23, 2022
Mathematics
integer
polynomial
coefficients
positive
coefficient
cubic
root
+
–
182
views
0
answers
Find all integers \(n\) for which the polynomial \(p(x)=x^5-n x-n-2\) can be represented as a product of two non-constant polynomials with integer coefficients.
Find all integers \(n\) for which the polynomial \(p(x)=x^5-n x-n-2\) can be represented as a product of two non-constant polynomials with integer coefficients.
MathsGee
Platinum
113k
points
MathsGee
asked
Sep 23, 2022
Mathematics
function
vector
polynomial
set
positive
coefficients
integer
+
–
389
views
0
answers
A function \(f: \mathbb{R} \rightarrow \mathbb{R}\) is bounded and satisfies
A function \(f: \mathbb{R} \rightarrow \mathbb{R}\) is bounded and satisfies\[f\left(x+\frac{1}{3}\right)+f\left(x+\frac{1}{2}\right)=(x)+f\left(x+\frac{5}{6}\right)\]for...
MathsGee
Platinum
113k
points
MathsGee
asked
Sep 23, 2022
Mathematics
function
bounded
value
positive
integer
theorem
taylor
+
–
384
views
0
answers
A function \(f: \mathbb{R} \rightarrow \mathbb{R}\) is bounded and satisfies
A function \(f: \mathbb{R} \rightarrow \mathbb{R}\) is bounded and satisfies\[f\left(x+\frac{1}{3}\right)+f\left(x+\frac{1}{2}\right)=(x)+f\left(x+\frac{5}{6}\right)\]for...
MathsGee
Platinum
113k
points
MathsGee
asked
Sep 22, 2022
Mathematics
function
bounded
value
positive
integer
theorem
taylor
+
–
188
views
0
answers
Find all values of \(a\) and \(b\) for which the soldier can visit every point of the lattice during his infinite walk.
Nonnegative integers \(a\) and \(b\) are given. A soldier is walking on the infinite lattice \(\mathbb{Z} \times \mathbb{Z}\) as follows. In each step, from a point \((x,...
MathsGee
Platinum
113k
points
MathsGee
asked
Sep 22, 2022
Mathematics
lattice
infinite
integer
soldier
+
–
322
views
0
answers
Let \(f(x)\) be a polynomial with integer coefficients. Let us assume that there exists a positive integer \(k\) and \(k\) consecutive integers \(n, n+1, \ldots, n+k-1\) such that . . .
Let \(f(x)\) be a polynomial with integer coefficients. Let us assume that there exists a positive integer \(k\) and \(k\) consecutive integers \(n, n+1, \ldots, n+k-1\) ...
MathsGee
Platinum
113k
points
MathsGee
asked
Sep 22, 2022
Mathematics
polynomial
integer
coefficients
positive
prove
+
–
557
views
0
answers
Given a positive integer \(a\), a function \(f\) from \(\mathbb{N}\) to \(\mathbb{R}\) satisfies \(f(a)=f(1995)\), \(f(a+1)=f(1996), f(a+2)=f(1997)\) and
Given a positive integer \(a\), a function \(f\) from \(\mathbb{N}\) to \(\mathbb{R}\) satisfies \(f(a)=f(1995)\), \(f(a+1)=f(1996), f(a+2)=f(1997)\) and\[f(n+a)=\frac{f(...
MathsGee
Platinum
113k
points
MathsGee
asked
Sep 22, 2022
Mathematics
function
positive
integer
theorem
taylor
bounded
value
+
–
316
views
1
answers
Show that there exists a positive multiple of 1996 whose sum of digits is 1996.
Show that there exists a positive multiple of 1996 whose sum of digits is 1996.
MathsGee
Platinum
113k
points
MathsGee
asked
Sep 22, 2022
Mathematics
numbers
digit
first
sum
three-digit
positive
integer
+
–
272
views
0
answers
Let \(n\) be a positive integer. A child builds a wall along a line with \(n\) identical cubes.
Let \(n\) be a positive integer. A child builds a wall along a line with \(n\) identical cubes. He lays the first cube on the line and at each subsequent step he lays the...
MathsGee
Platinum
113k
points
MathsGee
asked
Sep 22, 2022
Mathematics
positive
integer
child
builds
wall
identical
cubes
+
–
193
views
0
answers
Does there exist a base in which all the numbers \(10101,101010101,1010101010101\) ... are prime?
Does there exist a base in which all the numbers \(10101,101010101,1010101010101\) ... are prime?
MathsGee
Platinum
113k
points
MathsGee
asked
Sep 22, 2022
Mathematics
prove
prime
integer
exist
function
real
set
+
–
289
views
1
answers
If \(x\) and \(y\) are two positive numbers less than 1 , prove that
If \(x\) and \(y\) are two positive numbers less than 1 , prove that\[\frac{1}{1-x^2}+\frac{1}{1-y^2} \geq \frac{2}{1-x y}\]
MathsGee
Platinum
113k
points
MathsGee
asked
Sep 22, 2022
Mathematics
positive
number
integer
toys
cars
multiple
values
+
–
372
views
1
answers
State the power rule of differentiation with integer exponents
State the power rule of differentiation with integer exponents
AstraNova
Diamond
67.9k
points
AstraNova
asked
Sep 12, 2022
Mathematics
state
power
rule
differentiation
integer
exponents
+
–
471
views
0
answers
T/F: Let \(f\) be a position function. The average rate of change on \([a, b]\) is the slope of the line through the points \((a, f(a))\) and \((b, f(b))\)
T/F: Let \(f\) be a position function. The average rate of change on \([a, b]\) is the slope of the line through the points \((a, f(a))\) and \((b, f(b))\)
AstraNova
Diamond
67.9k
points
AstraNova
asked
Sep 12, 2022
Mathematics
function
bounded
integer
taylor
theorem
positive
points
+
–
571
views
1
answers
What is an integer?
What is an integer?
MathsGee
Platinum
113k
points
MathsGee
asked
Sep 7, 2022
Mathematics
prove
integer
numbers
equations
function
keywords
report
+
–
355
views
0
answers
What is a multiple of a number?
What is a multiple of a number?
MathsGee
Platinum
113k
points
MathsGee
asked
Aug 24, 2022
Mathematics
multiple
positive
integer
numbers
number
digit
value
+
–
323
views
0
answers
Let \(\mathrm{n} \geq 5\) be an integer. If \(9^{n}-8 n-1=64 \alpha\) and \(6^{n}-5 n-1=25 \beta\), then \(\alpha-\beta\) is equal to:
Let \(\mathrm{n} \geq 5\) be an integer. If \(9^{n}-8 n-1=64 \alpha\) and \(6^{n}-5 n-1=25 \beta\), then \(\alpha-\beta\) is equal to:
AstraNova
Diamond
67.9k
points
AstraNova
asked
Aug 15, 2022
Mathematics
function
positive
integer
theorem
taylor
bounded
prove
+
–
852
views
0
answers
If sum of coefficients in \(({x}-2 {y}+3 {z})^{{n}}\) is 128 then greatest coefficient in \((1+x)^{n}\) is
If sum of coefficients in \(({x}-2 {y}+3 {z})^{{n}}\) is 128 then greatest coefficient in \((1+x)^{n}\) is
AstraNova
Diamond
67.9k
points
AstraNova
asked
Aug 15, 2022
Mathematics
coefficient
cubic
positive
coefficients
integer
root
polynomial
+
–
559
views
1
answers
Prove that every integer \(n \geq 2\) is a product of prime numbers.
Prove that every integer \(n \geq 2\) is a product of prime numbers.
AstraNova
Diamond
67.9k
points
AstraNova
asked
Jul 29, 2022
Mathematics
prove
integer
product
prime
numbers
+
–
360
views
1
answers
Find the cubic polynomial, in \(x\), with integer coefficients that has \(\cos 20^{\circ}\) as a root. The coefficient of \(x^{3}\) should be positive, and the coefficients should have no common factor other than \(1 .\)
Find the cubic polynomial, in \(x\), with integer coefficients that has \(\cos 20^{\circ}\) as a root. The coefficient of \(x^{3}\) should be positive, and the coefficien...
AstraNova
Diamond
67.9k
points
AstraNova
asked
Jul 10, 2022
Mathematics
cubic
polynomial
integer
coefficients
root
coefficient
positive
+
–
469
views
1
answers
When the expression \(\left(2^{1}\right)\left(2^{2}\right)\left(2^{3}\right) \cdots\left(2^{99}\right)\left(2^{100}\right)\) is written as an integer, what is the product of the tens digit and the ones digit?
When the expression \(\left(2^{1}\right)\left(2^{2}\right)\left(2^{3}\right) \cdots\left(2^{99}\right)\left(2^{100}\right)\) is written as an integer, what is the product...
AstraNova
Diamond
67.9k
points
AstraNova
asked
Jul 10, 2022
Mathematics
expression
written
integer
product
digit
+
–
553
views
1
answers
The number of toy cars that Ray has is a multiple of 6 . When he loses two of them, the number of cars that he has left is a multiple of \(n\). If \(n\) is a positive even integer less than 10 , then how many possible values are there for \(n\) ?
The number of toy cars that Ray has is a multiple of 6 . When he loses two of them, the number of cars that he has left is a multiple of \(n\). If \(n\) is a positive eve...
AstraNova
Diamond
67.9k
points
AstraNova
asked
Jul 10, 2022
Mathematics
number
toys
cars
multiple
values
positive
integer
+
–
561
views
1
answers
Ray will choose at random an integer \(Q\), such that \(34<Q<43\). What is the probability that Ray will choose a prime number? Express your answer as a common fraction.
Ray will choose at random an integer \(Q\), such that \(34<Q<43\). What is the probability that Ray will choose a prime number? Express your answer as a common fraction.
AstraNova
Diamond
67.9k
points
AstraNova
asked
Jul 10, 2022
Mathematics
random
integer
prime
number
common
fraction
+
–
672
views
1
answers
A positive integer \(X\) is 2 more than a multiple of 3 . Its units digit is the same as the units digit of a number that is 4 more than a multiple of 5 . What is the smallest possible value of \(X\) ?
A positive integer \(X\) is 2 more than a multiple of 3 . Its units digit is the same as the units digit of a number that is 4 more than a multiple of 5 . What is the sma...
AstraNova
Diamond
67.9k
points
AstraNova
asked
Jul 8, 2022
Mathematics
positive
integer
multiple
digit
value
numbers
+
–
687
views
1
answers
For each integer \(n\), let \(f(n)\) be the sum of the elements of the \(n\)th row (i.e. the row with \(n+1\) elements) of Pascal's triangle minus the sum of all the elements from previous rows. For example,
For each integer \(n\), let \(f(n)\) be the sum of the elements of the \(n\)th row (i.e. the row with \(n+1\) elements) of Pascal's triangle minus the sum of all the elem...
AstraNova
Diamond
67.9k
points
AstraNova
asked
Jul 8, 2022
AI & Data Science
pascal
triangle
row
integer
pattern
+
–
391
views
1
answers
Find the smallest integer \(n\) for which the sum of the integers from \(-25\) to \(n\) (including \(-25\) and \(n\) ) is at least \(26 .\)
Find the smallest integer \(n\) for which the sum of the integers from \(-25\) to \(n\) (including \(-25\) and \(n\) ) is at least \(26 .\)
MathsGee
Platinum
113k
points
MathsGee
asked
Jul 7, 2022
Mathematics
find
smallest
integer
calculate
real
calculus
+
–
Page:
1
2
next »
This site uses cookies to provide quality services and to analyze traffic. For more information, see the
Privacy Policy
Register
Email or Username
Show
Hide
Password
I forgot my password
Remember
Log in
Register