Prove that if $x$ is divisible by $4$, then $x=a^2-b^2$
114393
If $a$ is divisible by $4$, then there exist int $b$ and $c$ such that $a = b^2 - c^2$
106847
Proof that $n^3+2n$ is divisible by $3$
52032
Prove that ${n^5 - n}$ is divisible by 5
64654
Suppose $a, b$ and $n$ are positive integers. Prove that $a^n$ divides $b^n$ if and only if $a$ divides $b$.
100305
Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
113359
Proving that $x^2 + 4$ is not divisible by $3$
102154
If $a$ and $b$ are consecutive integers, prove that $a^2 + b^2 + a^2b^2$ is a perfect square.
40626
Suppose that $ a,b \in \mathbb{Z}$ If 4 divides $ a^2 + b^2$, then $a$ and $b$ are not odd.
33011
Prove that the polynomial $f_n(x)=nx^{n+1}-(n+1)x^n+1$ is divisible by $(x-1)^2$
105832
prove that if $\gcd(a,b)=1$ then $\gcd(a^2, b^2)=1$
27281
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
153123
Proving by induction $4^n  0$
24098
Prove that $a$ divides $b$ and $b$ divides $a$ if and only if $a = \pm b$
11750
Prove that n is divisible by 4 in a cylic sum with variables which have only two possible values
102086
Prove a property of divisor function
118574
prove that $24 \mid a(a^2-1)$
116363
If $P(x^5)+xQ(x^5)+x^2R(x^5)=(x^4+x^3+x^2+x+1)S(x)$ , then prove that $P(x)$ is divisible by $x-1$