Prove: If u, v, w are integers such that $u^2 + v^2 = w^2$ , then $u$ and $v$ can’t be both odd.
13914
If $a^2+b^2=c^2$ then $a$ or $b$ is even.
18633
Prove every odd integer is the difference of two squares
134000
Proof by Strong Induction: $n = 2^a b,\, b\,$ odd, every natural a product of an odd and a power of 2
48038
If $z$ and $w$ are complex numbers such that $|(z+w)| = |(z-w)|$, prove that $\arg(z)-\arg(w) = \pm (\pi/2)$
59653
$x^2-y^2=2s$, s cannot be an odd integer
50250
Proving $\arg(zw)=\arg(z)+\arg(w)$
96097
Let $k$ be an odd positive integer. Prove that $(1+2+3...+n)|(1^k+2^k+3^k+...+n^k)$ for all positive integers $n$.
100399
A doubt with a part of a certain proof.
27063
Prove that if n is an odd positive integer , then $n^2\equiv1\mod8$
70619
Supposed $a,b \in \mathbb{Z}$. If $ab$ is odd, then $a^{2} + b^{2}$ is even.
151038
How to prove (A v B), (A → C), (B → D) therefore (C v D)
71361
Prove that $x^x+y^y=z^z$ doesn't have integer solutions
14576
$(U\cap W)^0 = U^0 + W^0$
6165
Proof by Induction $n^2+n$ is even
32524
Flawed proof that all positive integers are equal
81601
Prove that if $x$ is odd then $x^2 -1$ is divisible by $8$.
102168
Prove that there exists disjoint open subsets $U,V$ of $X$ such that $x \in U$ and $B \subseteq V$.