Prove that $5^{2^n}−1$ contains exactly $n+2$ factors $2$
109532
Proving $5^n \equiv 1 \pmod {2^r}$ when $n=2^{r-2}$
118372
Combination proof for $n(n+1)2^{n-2}=\sum_{k=1}^{n}k^2\binom{n}{k}$
44878
Factor $x^5+x^2+1$ into irreducible polynomials in $Z[x]$
100305
Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
49299
Proof by Induction: For any integer $n > 0$, $3|(5^{2n} − 1)$.
68480
Proof by Induction: Prove that $2^n > n^2$, for all natural numbers greater than or equal to $5$
9217
Find $n$ such that $x^2 + x + 1$ is a factor of $(x+1)^n - x^n - 1$.
142133
Prove that if $a^2 + b^2 = c^2$, then 5 divides abc. a,b,c are positive integers.
50894
Prove that $6$ divides $n(n + 1)(n + 2)$
112120
Find all primes of the form $2^{2^n} + 5$ for a nonnegative integer n
88628
Proving the total number of subsets of S is equal to $2^n$
47478
Show that any cyclic group of even order has exactly one element of order $2$
33996
Proving that $\gcd(2^m - 1, 2^n - 1) = 2^{\gcd(m,n )} - 1$
112631
Prove that if $d$ divides $n$, then $2^d -1$ divides $2^n -1$
35216
Prove $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5}):\mathbb{Q}$ is a simple extension
112575
Finding integer solutions of $m^2-n^5 = m - n$
120227
Proving $6^n - 1$ is always divisible by $5$ by induction