If a and b are odd integers, then $8\mid (a^2-b^2)$
66703
Show that $8 \mid (a^2-b^2)$ for $a$ and $b$ both odd
90283
Proof that $3 \mid \left( a^2+b^2 \right)$ iff $3 \mid \gcd \left( a,b\right)$
138894
Prove that if $3\mid(a^2+b^2)$,then $3\mid a$ and $ 3\mid b$
44182
Proving that an integer is even if and only if it is not odd
81601
Prove that if $x$ is odd then $x^2 -1$ is divisible by $8$.
20823
If $\gcd(a,b) = 1$ and $a,b\mid x$ then $ab\mid x$.
124995
$p\equiv 1,2,3\text{ mod }8 \Rightarrow p=a^2+2b^2\text{ for some $a,b\in\mathbb{Z}$.}$
24845
Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
31895
Prove that if $a$ and $b$ are odd, coprime numbers, then $\gcd(2^a +1, 2^b +1) = 3$
4141
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$
17047
Prove that if n is even then $n^2$ is even and if n is odd then $n^2$ is odd?
109245
α² is a cycle if and only if s is odd
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 $n$
140294
prove that $n >2$ and $n$ is a prime then $n$ is odd
49548
If $(a + ib)^3 = 8$, prove that $a^2 + b^2 = 4$
83307
If $n\mid a^2-1$, $n$ an odd integer, show $n = \gcd(a-1, n)\gcd(a+1, n)$
138846
Prove by induction that $3\mid n^4-n^2$ for all $n \in \mathbb{Z^+}$, $n\ge2$.