Pythagorean triple $(\xi,n,\zeta)$,prove that at least one of the numbers are divisible by $3,5$
26857
In any Pythagorean triplet at least one of them is divisible by $2$, $3$ and $5$.
113119
Use the division algorithm to prove that 3|(n³ + 2n) for all n ∈ ℕ
16176
Primitive Pythagorean triple divisible by 3
157294
Prove that if $n>1$ is odd, then $1^n+2^n+3^n+\ldots+(n-1)^n$ is divisible by $n$
10589
How to factorize $5$ in $\mathbb{Z}[\root 3 \of 2]$?
137808
$n^2 + 3n +5$ is not divisible by $121$
66578
Prove by induction that $2^{2n} – 1$ is divisible by $3$ whenever n is a positive integer.
30620
For which natural n is $3^n+5^n$ divisible by $3^{n-1}+5^{n-1}$?
125210
proof: primitive pythagorean triple, a or b has to be divisible by 3
83935
Using congruences, show $\frac{1}{5}n^5 + \frac{1}{3}n^3 + \frac{7}{15}n$ is integer for every $n$
9302
Questions about Divisibility of $2^n$ by $3$
4077
Using induction prove $n^3-n$ is divisible by 3 whenever n is a positive number.
46158
A positive integer is divisible by $3$ iff 3 divides the sum of its digits
20477
Prove that $\gcd(3^n-2,2^n-3)=\gcd(5,2^n-3)$
127833
Proving that $7^n(3n+1)-1$ is divisible by 9
132175
How many $5$-digit numbers with distinct digits are divisible by 3 (and generalize)
158210
showing $\arctan(\frac{2}{3}) = \frac{1}{2} \arctan(\frac{12}{5})$