How to prove if this equation provides an integral solution divisible by $3$?
89677
Why there isn't any integer solutions in non-zero integers for $z^3 = 3(x^3 +y^3+2xyz)$?
103197
number of distinct solution of Integral equation
54055
Proof $\prod_{i = 1}^n \frac{n + i}{2i-3} = 2^n(1-2n)$ using inducction
157294
Prove that if $n>1$ is odd, then $1^n+2^n+3^n+\ldots+(n-1)^n$ is divisible by $n$
128107
find all $ a \in \mathbb N $ such that $2^a − 1 \equiv 0 \pmod 3$ and $ 4x^2 + 1 \equiv 0 \pmod {\frac{2^a -1}{3}}$ has a solution
2491
For $0 < x < \pi/2 $, prove that $x + \frac{x^{3}}{3} <\tan x $
136700
Proving divisibility of expression using induction
89265
Proving that $x - \frac{x^3}{3!} 0$
85959
How do I prove that among any $5$ integers, you are able to find $3$ such that their sum is divisible by $3$?
94067
How prove this diophantine equation $x^2+y^2+z^3=n$ always have integer solution
100892
Proving divisibility of $a^3 - a$ by $6$
10635
diophantine equations $x^3-2y^3=1$
108801
Given that $xyz=1$, prove that $\frac{x}{1+x^4}+\frac{y}{1+y^4}+\frac{z}{1+z^4}\le \frac{3}{2}$
92692
Prove $3(x^2y+y^2z+z^2x)(xy^2+yz^2+zx^2)\ge xyz(x+y+z)^3$
4077
Using induction prove $n^3-n$ is divisible by 3 whenever n is a positive number.
113119
Use the division algorithm to prove that 3|(n³ + 2n) for all n ∈ ℕ
157884
For any prime $p>3$ show that 3 divides $2p^2+1$