Prove that $n=\frac{5^{125}-1}{5^{25}-1}$ is a composite number
60462
Prove that $\frac{ 5^{125}-1}{ 5^{25}-1}$ is a composite number
66861
Show that $11^{10} \equiv 1 (\mod 100)$
19701
Prove $5\mid2^{4n}-1$ by induction
117775
Combinatorial proof of a Stirling number identity.
45460
Proof verification of a number theory problem involving sequences.
280
Prove by induction that $5^n - 1$ is divisible by $4$.
27963
How many ways a composite number can be resolved into two factors which are prime to each other?
31344
Proving $2^{2^n}+3^{2^n}+5^{2^n}$ is divisible by $19$ for all $n\geq 1$ by induction
53378
$\max(\{n: n+5 | n^5 + 5\})$
52800
Show that $z^5-1=(z-1)(z^2+2z\cos{\pi \over 5}+1)(z^2-2z\cos{2\pi \over 5}+1)$
75685
Prove that there is prime number and natural so $n\times q$ digits are $1$.
48503
Proving : $ \bigl(1+\frac{1}{n+1}\bigr)^{n+1} \gt (1+\frac{1}{n})^{n} $
49299
Proof by Induction: For any integer $n > 0$, $3|(5^{2n} − 1)$.
3611
How to prove $n^5 - n$ is divisible by $30$ without reduction
6561
Prove that the expression $5^{2n+1} \cdot 2^{n+2} + 3^{n+2} \cdot 2^{2n+1}$ is divisible by 19.
112595
Prove that the limit of this sequence is $\frac{1}{2}(1 + \sqrt{5})$
138614
Proof concerning Stirling numbers of the first kind