Prove that for any two integers $a$ and $b$ $ab(a^{60}-b^{60}) $ is divisible by $56786730$
20504
$\forall m,n \in \Bbb N$ : $\ 56786730\mid mn(m^{60}-n^{60})$
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
19046
Show that if $a$ and $b$ are positive integers with $(a,b)=1$ then $(a^n, b^n) = 1$ for all positive integers n
151434
If integers $a$ and $b$ are not both zero, then $\gcd(a,b)=\gcd(a-b,b)$
71625
Divisibility question
35666
How to prove the divisibility rule for $3\, $ [casting out threes]
24160
Show that if $a$ is an odd integer and $b$ is an even integer then $\gcd(a,b)=\gcd(a,b/2)$
48404
If $a$ and $b$ are integers such that $9$ divides $a^2 + ab + b^2$ then $3$ divides both $a$ and $b$.
49501
Prove that : $(a-b)(a-c)(a-d)(b-c)(b-d)(c-d)$ divisible by $12$
68145
If $p$ is an odd prime and $k$ an integer with $0<k<p-1$ then $1^k + 2^k + \ldots + (p-1)^k$ is divisible by $p$
116970
On the number divisors of a number
11168
Proof of divisibility: if $a|b$ and $a|(b+c)$ then $a|c$
122019
Prove by mathematical induction that $2^{3^n}+1$ is divisible by $3^{n+1}$
106847
Proof that $n^3+2n$ is divisible by $3$
87379
How to prove that $2^{n+2}+3^{2n+1}$ is divisible by 7 using induction?
115866
Proof by induction; $a^n$ divides $b^n$ implies $a$ divides $b$
125210
proof: primitive pythagorean triple, a or b has to be divisible by 3