Proving divisibility of $a^3 - a$ by $6$
65430
Using the Well Ordering Principle to Show that n^3 - n is divisible by 6.
29963
$6$ divides $a+b+c$ if and only if $6$ divides $a^{3}+b^{3}+c^{3}$
150528
Pythagorean triples $(a,b,c)$ and divisibility of $a$ or $b$ by $3$.
38904
Prove that $(a + b + c)^{13}$ is divisible by $abc$ if $b|a^3$, $c|b^3$ and $a|c^3$.
120954
Prove that: $\sqrt[3]{a_1^3+ a_2^3 +\cdots+a_n^3} \le \sqrt{a_1^2 + a_2^2 +\cdots+a_n^2}$
48484
Prove that $6|a+b+c$ if and only if $6|a^3+b^3+c^3$
16176
Primitive Pythagorean triple divisible by 3
35666
How to prove the divisibility rule for $3\, $ [casting out threes]
125855
Prove: The product of any three consecutive integers is divisible by $6$.
56760
Prove by induction that an expression is divisible by 11
80365
Prove that $n$ is divisible by $6$
138894
Prove that if $3\mid(a^2+b^2)$,then $3\mid a$ and $ 3\mid b$
26301
Prove that $x^3 \equiv x \bmod 6$ for all integers $x$
113119
Use the division algorithm to prove that 3|(n³ + 2n) for all n ∈ ℕ
47232
Prove $\forall a,b,c \in \mathbb Z$, if $ab+ac\equiv 3\pmod 6$ then $b \not\equiv c \pmod 6$ by contraposition
78416
Show that $7$ divides $a^{15}-a^3$ for any integer $a$
81058
Evaluate $6^{433} \pmod {21}$ and a proving question