New posts in Divisibility

Find a counterexample: For every antiprime $n>1$, there is a prime divisor $p$ such that $n/p$ is an antiprime

A generalization of the (in)famous IMO 1988 problem 6: If $\frac{a^2 + b^2 - abc}{ab + 1}$ is a positive integer then it is a square.

Find all solutions in $\mathbb{N}$ to $a^a=a^b+b^a$

Is there a prime every year if YYYYMMDD is treated as a base-$10$ number?

Remainder Theorem Question: Deduce the Polynomial Given the Remainder

Finding remainder when $5^{99}$ is divided by $13$

Prove that, if $p$ is an odd prime number, then ${f(p)}=\binom{2p-1}{p-1}-1$ is divisible by $p^2$

Prove that numbers of the form 131, 1331, 13331, ... are divisible by 19 when they have length 15+18k

Prove by mathematical induction that $(3n+1)7^n -1$ is divisible by $9$ for integral $n>0$

Solutions $a,b,c \mid 1+a+b+c $ over positive integers algebraically (avoiding brute force)?