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

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

The right digit of 4th power of any natural number

July 22nd, 2022

Last digit of a perfect square must be $0, 1, 4, 5, 6,$ or $9$

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

Is this a solution for the problem: $\ a^3 + b^3 = c^3\ $ has no nonzero integer solutions?

July 30th, 2022

Prove or disprove: If $a\mid (b+c)$, then either $a\mid b$ or $a\mid c$

August 7th, 2022

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

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

November 4th, 2020

Is this the general solution of finding the two original squares that add up to a given integer N?

August 1st, 2022

Greatest Common Divisor of prime numbers

September 18th, 2020

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

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

Finding last two non-zero digits of 2016!

August 1st, 2022

$x^4 = -1$ (mod $p$) implies p = 1 mod 8

August 1st, 2022

Proof by induction with a prime number

August 1st, 2022

Find the pairs $(x,y) ; 0 \le x,y \le 18$ such that $19 \vert 3x+4y+5$

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

how to prove that $n(n+1)$ can't be square?

August 1st, 2022