Simple proof of $x^n−y^n=(x−y)(x^{n−1}+x^{n−2}y+…+xy^{n−2}+y^{n−1})$
46751
Power rule step. Where does equation of the difference of two numbers raised to the same power come from?
71756
diophantine equation: $x^2 +y^2 = z^n$
41383
Prove that $(x+y+z)^2(yz+zx+xy)^2 \leq 3(y^2+yz+z^2)(z^2+zx+x^2)(x^2+xy+y^2)$
42677
Proving $(\alpha + \beta)^{p^n} = \alpha^{p^n} + \beta^{p^n}$ in a finite field
17176
Proof that $x^n \mod b = (x \mod b)^n$
74835
how to prove that $ \lim x_n^{y_n}=\lim x_n^{\lim y_n}$?
135747
Prove $x^{rs}-1=(x^s-1)(x^{s(r-1)}+...+x^s+1)$
148330
Induction Proof for $F_{2n} = F^2_{n+1} - F^2_{n-1}$
48333
Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$
108382
Prove $x^n-1$ is divisible by $x-1$ by induction
115799
Proving $x^{\log n} = n^{\log x}$
114074
Intuitive/Visual proof that $(1+2+\cdots+n)^2=1^3+2^3+\cdots+n^3$
92784
Intuitive (combinatorial) proof of $2^n=\sum_{k=0}^n {n\choose k}$
118372
Combination proof for $n(n+1)2^{n-2}=\sum_{k=1}^{n}k^2\binom{n}{k}$
16177
Proof by Induction: $\sum_0^nx^i=(1-x^{n+1})/(1-x)$
153123
Proving by induction $4^n  0$
1139
Combinatorial proof of $\sum_{j=0}^{k} \binom{n}{j} = \sum_{j=0}^k \binom{n-1-j}{k-j}2^j$