Prove that $a^2+b^2$ and $a^2-b^2$ are relatively prime
15168
If $a,b$ are positive integers such that $\gcd(a,b)=1$, then show that $\gcd(a+b, a-b)=1$ or $2$. and $\gcd(a^2+b^2, a^2-b^2)=1$ or $2 $
77070
Prove Euler's Theorem when the integers are not relatively prime
37913
Prove that $ AB$ is a subgroup of order $mn$ if $m$ and $n$ are relatively prime.
6777
Showing $(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$
10403
Let $p$ be a prime integer. Show that for each $a ∈ GF(p)$ there exist elements $b$ and $c$ of $GF(p)$ satisfying $a = b^2 + c^2$.
95588
Prove by Contradiction: if $4\mid a^2 + b^2$, then $a$ and $b$ are not both odd
90144
Show that if $a+bi$ is irreducible over $\mathbb{Z} [i]$ then $a^2 + b^2$ is prime over $\mathbb{Z} $
142133
Prove that if $a^2 + b^2 = c^2$, then 5 divides abc. a,b,c are positive integers.
13478
Prove that if $a^p-b^p$ is divisible by $p$, then it is also divisible by $p^2$
72470
Prove that $2|ab| \leq a^2 + b^2$ and $|a|+|b| \leq \sqrt {2}(a^2+b^2)^{1/2}$
115460
Proving $a\mid b^2,\,b^2\mid a^3,\,a^3\mid b^4,\ldots\implies a=b$ - why is my approach incorrect
8366
Proof of $a^n+b^n$ divisible by $a+b$ when $n$ is odd
15191
If $a^2$ divides $b^2$, then $a$ divides $b$
103496
Show that $3p^2=q^2$ implies $3|p$ and $3|q$
20964
Proof that $n^2 < 2^n$
94516
If $3$ divides $a^2 + b^2$, then $3$ divides $a$ and $3$ divides $b$
37808
Show that $\gcd(a^2, b^2) = \gcd(a,b)^2$