Find all positive integers $m$ that satisfies: $a^2 \equiv 0\mod{m} \Rightarrow a \equiv 0 \mod{m}$, $\forall a \in \mathbb{Z}$
134365
When is this true: If $m^2$ is a multiple of N then m is a multiple of N
52951
Find all $n \in \mathbb{Z^+}$ such that $\phi(n)=4$
50927
If $m,n\in N$ Prove that there is such a positive integer k, such that $(\sqrt{m}+\sqrt{m+1})^n=\sqrt{k}+\sqrt{k+1}$
59535
Prove that there exists such a set of $n$ positive integers
38882
If $n$ is a positive integer such that $n^3 − n − 6 = 0$, then, for every positive integer $m$ with $m \not = n$, $m^3 − m − 6 \not = 0$.
46147
Proving $(\forall a\in\mathbb{Z^+})(m\in\mathbb{Z^+}\to a^m\equiv a^{m-\phi(m)}\pmod{m})$
34668
Find all rings $R$ satisfying $\mathbb Z \subset R \subset \mathbb Z[\frac {1}{2}]$
151225
Solved Problems in Algebraic Number Theory
44033
Number theory lemma - $x^2 \equiv 1 \pmod p$ implies $x\equiv\pm 1\pmod p$
77024
Find the number of solutions of $x^2=x\mod m$ for any integer $m$
20834
Integer solutions to $c=a^2-b^2$
513
If n is an odd integer, show there exists a positive integer k such that 2^k mod n = 1.
119582
How to select the right modulus to prove that there do not exist integers $a$ and $b$ such that $a^2+b^2=1234567$?
51153
Number of solutions to $x^2\equiv a\pmod m$
155363
Find all integers $(x, y)$ such that $1 + 2^x + 2^{2x + 1} = y^2$
28861
Given an invertible matrix $A$ such that all elements in $A$ and in $𝐴^{−1}$ are integers, find $|𝐴^4|$
53915
prove that $a \equiv b \mod m$ is an equivalence relation on the integers