Prove that if (a,b,c) is a Pythagorean triple, then 3 divides either $a$ or $b$ without remainder classes
96737
Geometric proof that a Pythagorean triple has a number divisible by $3$?
130653
$p^2$ divides $ab$ and $\gcd(a,b)=1$. Show $p^2$ divides $a$ or $p^2$ divides $b$
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
82777
If $\gcd(a, b) = 1$ then prove that $\gcd(a+b, a^2-ab+b^2) = 1$ or $3$?
118809
If $a$ divides $bc$ and $\gcd(a,b) = d$ then $\frac a d$ divides c
139082
If $a,b,c>0$ and $a^3+b^3=c^3$ then prove that $a^2+b^2-c^2>6(c-a)(c-b)$.
72670
Find three distinct triples (a, b, c) consisting of rational numbers that satisfy $a^2+b^2+c^2 =1$ and $a+b+c= \pm 1$.
37529
If $\sqrt[3]{a} + \sqrt[3]{b}$ is rational then prove $\sqrt[3]{a}$ and $\sqrt[3]{b}$ are rational
114780
$\forall a,b,c \in \mathbb{N}\!:\ a\mid b \Rightarrow ac\mid bc. $ Divisibility Proof
18772
If $a,b \in\mathbb N$ and $\gcd(a,b)=1$, prove that $\gcd(a+b;a^2+b^2)= 1$ or $2$.
151038
How to prove (A v B), (A → C), (B → D) therefore (C v D)
104124
Prove or disprove: $A-(B-C) = (A-B)-C$
38904
Prove that $(a + b + c)^{13}$ is divisible by $abc$ if $b|a^3$, $c|b^3$ and $a|c^3$.
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
29971
Let $a,b,c$ positive integers such that $\left(1+\frac{1}{a}\right)\left(1+\frac{1}{b}\right)\left(1+\frac{1}{c}\right) = 3$. Find those triples.
115866
Proof by induction; $a^n$ divides $b^n$ implies $a$ divides $b$
54699
Product of pairwise coprime integers divides $b$ if each integer divides $b$