Prove the following statement: if $ab$ is odd, then $a^2 + b^2$ is even
70619
Supposed $a,b \in \mathbb{Z}$. If $ab$ is odd, then $a^{2} + b^{2}$ is even.
103116
Prove that any odd number can be a leg in a Pythagorean Triple
79219
Prove that $a^{2^n} \equiv 1 \pmod{2^{n+2}},$ where $a$ is an odd integer.
84946
If $0<a<b$, prove that $a<\sqrt{ab}<\frac{a+b}{2}<b$
129680
Prove that $n$ is even.
94570
Proof that every odd integer is a difference of two squares
31783
Is this proof of $ab = 0$ correct?
15191
If $a^2$ divides $b^2$, then $a$ divides $b$
127891
If $ a^{2} + b^{2} = c^{2}$ and $c$ is even, prove that $a$ and $b$ are both even.
72470
Prove that $2|ab| \leq a^2 + b^2$ and $|a|+|b| \leq \sqrt {2}(a^2+b^2)^{1/2}$
66703
Show that $8 \mid (a^2-b^2)$ for $a$ and $b$ both odd
134000
Proof by Strong Induction: $n = 2^a b,\, b\,$ odd, every natural a product of an odd and a power of 2
5729
If $a^2+b^2+c^2=1$ then prove the following.
157294
Prove that if $n>1$ is odd, then $1^n+2^n+3^n+\ldots+(n-1)^n$ is divisible by $n$
118507
Prove $\frac{ab}{1+c^2}+\frac{bc}{1+a^2}+\frac{ca}{1+b^2}\le\frac{3}{4}$ if $a^2+b^2+c^2=1$
40030
FA that accepts odd number of $b$ and even number of $a$
87522
If $ a + b + c \mid a^2 + b^2 + c^2$ then $ a + b + c \mid a^n + b^n + c^n$ for infinitely many $n$