Prove that $2^q+q^2$ is divisible by 3 where $q$ is a prime and $q\geq5$.
112541
Prove that $n^2 + 2^n$ is composite if $n\not\equiv3\pmod{6}$.
90916
Prove that if $3\mid a^2+b^2$ then $3\mid a$ and $3\mid b$.
11216
Induction: How to prove that $ab^n+cn+d$ is divisible by $m$.
42376
Let $p$ be prime and $(\frac{-3}p)=1$. Prove that $p$ is of the form $p=a^2+3b^2$
10744
Prove that a number is divisible by 3 iff the sum of its digits is divisible by 3
157294
Prove that if $n>1$ is odd, then $1^n+2^n+3^n+\ldots+(n-1)^n$ is divisible by $n$
44440
Prove $\sqrt{2}+\sqrt[3]{5}$ is irrational
139269
Prove that $2n-3\leq 2^{n-2}$ , for all $n \geq 5$ by mathematical induction
8366
Proof of $a^n+b^n$ divisible by $a+b$ when $n$ is odd
39642
Efficient way to find $[\mathbb{Q}(\sqrt{5}, \sqrt{3}, \sqrt{2}): \mathbb{Q}(\sqrt{3}, \sqrt{2})]$
87282
Diophantine equation involving prime numbers : $p^3 - q^5 = (p+q)^2$
15348
prime divisor of $3n+2$ proof
144814
If $p$ and $q$ are primes, which binomial coefficients $\binom{pq}{n}$ are divisible by $pq$?
85959
How do I prove that among any $5$ integers, you are able to find $3$ such that their sum is divisible by $3$?
35666
How to prove the divisibility rule for $3\, $ [casting out threes]
94516
If $3$ divides $a^2 + b^2$, then $3$ divides $a$ and $3$ divides $b$
138894
Prove that if $3\mid(a^2+b^2)$,then $3\mid a$ and $ 3\mid b$