Prove for any integer $a$, one of the integers $a$, $a+2$, $a+4$ is divisible by $3$.
40565
How can I prove that one of $n$, $n+2$, and $n+4$ must be divisible by three, for any $n\in\mathbb{N}$
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 $a=b$
46158
A positive integer is divisible by $3$ iff 3 divides the sum of its digits
8366
Proof of $a^n+b^n$ divisible by $a+b$ when $n$ is odd
13478
Prove that if $a^p-b^p$ is divisible by $p$, then it is also divisible by $p^2$
62100
Show that $n^3-n$ is divisible by $6$ using induction
122019
Prove by mathematical induction that $2^{3^n}+1$ is divisible by $3^{n+1}$
27428
Divisibility test for $4$
125210
proof: primitive pythagorean triple, a or b has to be divisible by 3
74561
Let $a_1,a_2,\cdots,a_n$ be $n$ numbers such that $a_i$ is either $1$ or $-1$.If $a_1a_2a_3a_4+\cdots+a_na_1a_2a_3=0$ then prove that $4\mid n$.
114873
Show that if $n$ is not divisible by $2$ or by $3$, then $n^2-1$ is divisible by $24$.
41563
Prove that if the sum of digits of a number is divisible by 3, so is the number itself.
79940
$\binom{p}{i}$ divisible by $p$, with $p$ prime
11750
Prove that n is divisible by 4 in a cylic sum with variables which have only two possible values
66578
Prove by induction that $2^{2n} – 1$ is divisible by $3$ whenever n is a positive integer.
82774
Prove by mathematical induction that $n^3 - n$ is divisible by $3$ for all natural number $n$
35666
How to prove the divisibility rule for $3\, $ [casting out threes]