Suppose that $ a,b \in \mathbb{Z}$ If 4 divides $ a^2 + b^2$, then $a$ and $b$ are not odd.
95588
Prove by Contradiction: if $4\mid a^2 + b^2$, then $a$ and $b$ are not both odd
118452
how to prove $\mathbb Z_n$ has divisors of zero if and only if $n$ is not prime
4396
If $A^2\succ B^2$, then necessarily $A\succ B$
2771
A group has odd number of elements iff each element is a square, $a=b^2$.
88982
Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
21006
Let $a,b$ be positive integers such that $a\mid b^2 , b^2\mid a^3 , a^3\mid b^4 \ldots$ so on , then $a=b$?
113359
Proving that $x^2 + 4$ is not divisible by $3$
155784
If $\gcd(a, b) = 1$ and if $ab = x^2$, prove that $a, b$ must also be perfect squares; where $a,b,x$ are in the set of natural numbers
142133
Prove that if $a^2 + b^2 = c^2$, then 5 divides abc. a,b,c are positive integers.
115866
Proof by induction; $a^n$ divides $b^n$ implies $a$ divides $b$
37596
If $\gcd(a,b)= 1$ and $a$ divides $bc$ then $a$ divides $c\ $ [Euclid's Lemma]
153313
Prove that for all integers $ a $ and $ b $, if $ a $ divides $ b $, then $ a^{2} $ divides $ b^{2} $.
49548
If $(a + ib)^3 = 8$, prove that $a^2 + b^2 = 4$
135241
Show that $\mathbb{Z}/n^2\mathbb{Z}$ is not isomorphic to other group
12927
$A^2+B^2=AB$ and $BA-AB$ is non-singular
149071
Let $d$ be any positive integer not equal to $2, 5,$ or $ 13$ , then $\exists a, b \in \{2, 5, 13, d\}$ such that $ab − 1$ is not a perfect square?
7491
How to show that $7\mid a^2+b^2$ implies $7\mid a$ and $7\mid b$?