# New post in Elementary-number-theory

July 26th, 2022

## 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

## Prove $n^3$ has the form $9k$ or $9k + 1$ or $9k + 8$ for some integer $k$.

December 26th, 2022

## Find the remainder when $9^{16} - 5^{16}$ is divided by $14$.

December 22nd, 2022

## Prove: For a,b,c positive integers, ac divides bc if and only if a divides b

December 10th, 2022

## Suppose $(a,b)=1$. If $a$ divides $c$ and $b$ divides $c$ prove that $ab$ divides $c$

December 9th, 2022

## What is the highest common factor of $n$ and $2n + 1$

December 6th, 2022

## Numbers of relatively primes

August 15th, 2022

July 22nd, 2022

July 22nd, 2022

## Part A: Prove that $(k, n+k) = 1$ if and only if $(k, n)= 1$

October 11th, 2022

## general formula using informal inductive reasoning

October 15th, 2022

## The sum of all the odd numbers to infinity

August 10th, 2022

## Find $n$ such that $n/2$ is a square, $n/3$ is a cube, and $n/5$ a fifth power

September 12th, 2022

July 30th, 2022

August 7th, 2022

August 9th, 2022

## Find all positive integers $n$ such that $n^4 − 1$ is divisible by 5.

November 4th, 2020

August 1st, 2022

## Greatest Common Divisor of prime numbers

September 18th, 2020

March 5th, 2020

## Show that: $97\mid (2^{48})-1$

December 31st, 2020

## Solve $y^3=x^{3}+8x^{2}-6x+8$ for positive integers $x, y$

September 16th, 2020

August 1st, 2022

August 1st, 2022

August 1st, 2022

August 1st, 2022

## If $\gcd(a,b) = 1$, show that $\gcd(2a+b, a+2b)=1 \mbox{ or } 3$

January 22nd, 2021

## The sum of two squares is zero

October 9th, 2020

August 1st, 2022