Let a,b be integers. Then $3 | a^2 + b^2$ if and only if 3 | a and 3 | b
90916
Prove that if $3\mid a^2+b^2$ then $3\mid a$ and $3\mid b$.
152693
If $C|a$ and $C|b$ then $C|(ax+by)$
114185
Existence of $x$ such that $2^x =a,3^x=b,5^x=c$ for some integers $a,b,c$
30261
How can I find all integers $x≠3$ such that $x−3|x^3−3$
18693
If $a,b$ are positive integers such that $a^{n}+n$ divides $b^{n}+n$ for every $n$, then $a=b$
99692
Prove that $a^3+b^3+c^3 \geq a^2b+b^2c+c^2a$
60842
if $a^2+b^2=c^2$ then $gcd(a,b)=gcd(a,c)=gcd(b,c)$.
136854
Prove: For a,b,c positive integers, ac divides bc if and only if a divides b
80148
Prove $\gcd(a+b,a^2+b^2)$ is $1$ or $2$ if $\gcd(a,b) = 1$
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
63774
If a and b are odd integers, then $8\mid (a^2-b^2)$
89184
Prove $30|(a^3b-ab^3) $
121700
If $a$ and $b$ are positive real numbers, then $a + b \geq 2 \sqrt{ab}$.
66261
Inequalities help: $(a^3+b^3)^2\leq (a^2+b^2)(a^4+b^4)$
11506
Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when it's an integer
48484
Prove that $6|a+b+c$ if and only if $6|a^3+b^3+c^3$
139082
If $a,b,c>0$ and $a^3+b^3=c^3$ then prove that $a^2+b^2-c^2>6(c-a)(c-b)$.