Prove $(n-1)^2 | (n^m-1) \iff (n-1)| m$.
9997
For what powers $k$ is the polynomial $n^k-1$ divisible by $(n-1)^2$?
49750
Proof of the square root inequality $2\sqrt{n+1}-2\sqrt{n}<\frac{1}{\sqrt{n}}<2\sqrt{n}-2\sqrt{n-1}$
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
73002
For $n \geq 2$, prove that $(1- \frac{1}{4})(1- \frac{1}{9})(1- \frac{1}{16})...(1- \frac{1}{n^2}) = \frac{n+1}{2n}$
20964
Proof that $n^2 < 2^n$
27281
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
76696
Using induction to prove $2^{n-1}(1 + a_1a_2\ldots a_n) \geq (1+a_1)(1+a_2)\ldots(1+a_n)$ for $a_i \geq 1$
119436
Proving $2^n\leq 2^{n+1}-2^{n-1}-1$ for all $n\geq 1$ by induction
25004
Proving $\binom{m}{n} + \binom{m}{n-1} = \binom{m+1}{n}$ algebraically
11693
If $p \mid m^p+n^p$ prove $p^2 \mid m^p+n^p$
146093
Why if $n \mid m$, then $(a^n-1) \mid (a^m-1)$?
25419
If $n\geq m$ then $(x^m+y^m)^{1/m} \ge (x^n+y^n)^{1/n}$
112631
Prove that if $d$ divides $n$, then $2^d -1$ divides $2^n -1$
148330
Induction Proof for $F_{2n} = F^2_{n+1} - F^2_{n-1}$
90962
For positive integers $m,n$ if $\sqrt 7 - \frac{m}{n} > 0$ then prove that $\sqrt 7 - \frac{m}{n} > \frac{1}{{mn}}$
4315
show that if $n\geq1$, $(1+{1\over n})^n<(1+{1\over n+1})^{n+1}$
85731
Prove by induction that $n! > n^2$