proof for $1=1^2$ ,$1+3=4=2^2$,$1+3+5=9=3^2$,$1+3+5+7=16=4^2$
71736
I found this odd relationship, $x^2 = \sum_\limits{k = 0}^{x-1} (2k + 1)$.
54055
Proof $\prod_{i = 1}^n \frac{n + i}{2i-3} = 2^n(1-2n)$ using inducction
112147
Proving $9$ divides $n^3 + (n+1)^3 + (n+2)^3$
65280
If $a, b, c >0$ prove that $ [(1+a)(1+b)(1+c)]^7 > 7^7a^4b^4c^4 $.
97057
Show $a^2+b^2+c^2=1$ $\implies$ $ \dfrac {b^2c^2}{1+a^2} +\dfrac {c^2a^2}{1+b^2}+\dfrac {a^2b^2}{1+c^2} \le \dfrac 14 $
96894
Prove $f_{n+1}^2+f_n^2=f_{2n+1}$
34059
$(a^{2^n}+1,a^{2^m}+1)=1 or 2$
44940
Proving by induction that $1^3 + 2^3 + 3^3 + \ldots + n^3 = \left[\frac{n(n+1)}{2}\right]^2$
118372
Combination proof for $n(n+1)2^{n-2}=\sum_{k=1}^{n}k^2\binom{n}{k}$
70625
Prove By Induction $1 + 1/2 + 1/3 + ... + 1/(2^n) ≥ 1 + n/2$
89175
Proof of $(a+b)^{n+1}$
87379
How to prove that $2^{n+2}+3^{2n+1}$ is divisible by 7 using induction?
20705
On equations $m^2+1=5^n$
141371
Prove that $\alpha^n+\beta^n+\gamma^n \equiv 4^n+5^n+(-6)^n \pmod{17}$
99052
Prove that $( 1 + n^{-2}) ^n \to 1$.
27304
Proving $ 1+\frac{1}{4}+\frac{1}{9}+\cdots+\frac{1}{n^2}\leq 2-\frac{1}{n}$ for all $n\geq 2$ by induction
80148
Prove $\gcd(a+b,a^2+b^2)$ is $1$ or $2$ if $\gcd(a,b) = 1$