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Elementary-number-theory
New post in Elementary-number-theory
Find all positive integers $a$ and $b$ satisfying $\gcd (a,b)=10$ and $\operatorname{lcm} (a,b)=100$ simultaneously.
July 26th, 2022
elementary-number-theory
least-common-multiple
gcd-and-lcm
number-theory
Show that 5n + 3 and 7n + 4 are relatively prime for any n 2 N. Show that s and t are not unique.
January 5th, 2023
elementary-number-theory
coprime
Prove $n^3$ has the form $9k$ or $9k + 1$ or $9k + 8$ for some integer $k$.
December 26th, 2022
elementary-number-theory
Find the remainder when $9^{16} - 5^{16}$ is divided by $14$.
December 22nd, 2022
divisibility
elementary-number-theory
Prove: For a,b,c positive integers, ac divides bc if and only if a divides b
December 10th, 2022
divisibility
elementary-number-theory
Suppose $(a,b)=1$. If $a$ divides $c$ and $b$ divides $c$ prove that $ab$ divides $c$
December 9th, 2022
proof-writing
elementary-number-theory
What is the highest common factor of $n$ and $2n + 1$
December 6th, 2022
gcd-and-lcm
least-common-multiple
elementary-number-theory
Numbers of relatively primes
August 15th, 2022
inclusion-exclusion
elementary-number-theory
The right digit of 4th power of any natural number
July 22nd, 2022
elementary-number-theory
Last digit of a perfect square must be $0, 1, 4, 5, 6,$ or $9$
July 22nd, 2022
elementary-number-theory
Part A: Prove that $(k, n+k) = 1$ if and only if $(k, n)= 1$
October 11th, 2022
elementary-number-theory
general formula using informal inductive reasoning
October 15th, 2022
discrete-mathematics
induction
elementary-number-theory
The sum of all the odd numbers to infinity
August 10th, 2022
paradoxes
sequences-and-series
elementary-number-theory
summation
Find $n$ such that $n/2$ is a square, $n/3$ is a cube, and $n/5$ a fifth power
September 12th, 2022
elementary-number-theory
Is this a solution for the problem: $\ a^3 + b^3 = c^3\ $ has no nonzero integer solutions?
July 30th, 2022
diophantine-equations
elementary-number-theory
number-theory
proof-verification
Prove or disprove: If $a\mid (b+c)$, then either $a\mid b$ or $a\mid c$
August 7th, 2022
elementary-number-theory
If an integer a is such that a-2 is divisible by 3 then a^2-1 is divisible by 3. prove by direct method
August 9th, 2022
elementary-number-theory
divisibility
Find all positive integers $n$ such that $n^4 − 1$ is divisible by 5.
November 4th, 2020
divisibility
elementary-number-theory
modular-arithmetic
Is this the general solution of finding the two original squares that add up to a given integer N?
August 1st, 2022
elementary-number-theory
sums-of-squares
Greatest Common Divisor of prime numbers
September 18th, 2020
elementary-number-theory
gcd-and-lcm
When a prime number p divides $ab$ then we have either p divides a or p divides b.Prove that $\sqrt {p} $ is not rational for any prime number p.
March 5th, 2020
irrational-numbers
prime-numbers
elementary-number-theory
Show that: $97\mid (2^{48})-1$
December 31st, 2020
elementary-number-theory
Solve $y^3=x^{3}+8x^{2}-6x+8$ for positive integers $x, y $
September 16th, 2020
elementary-number-theory
diophantine-equations
Finding last two non-zero digits of 2016!
August 1st, 2022
elementary-number-theory
factorial
$x^4 = -1$ (mod $p$) implies p = 1 mod 8
August 1st, 2022
number-theory
prime-numbers
elementary-number-theory
Proof by induction with a prime number
August 1st, 2022
induction
elementary-number-theory
Find the pairs $(x,y) ; 0 \le x,y \le 18$ such that $19 \vert 3x+4y+5$
August 1st, 2022
number-theory
elementary-number-theory
divisibility
If $\gcd(a,b) = 1$, show that $\gcd(2a+b, a+2b)=1 \mbox{ or } 3$
January 22nd, 2021
arithmetic
elementary-number-theory
The sum of two squares is zero
October 9th, 2020
elementary-number-theory
algebra-precalculus
how to prove that $n(n+1)$ can't be square?
August 1st, 2022
elementary-number-theory
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