Logical argument for $(1+2+\dots+n)^2=1^3+2^3+\dots+n^3$
15100
Proving the identity $\sum_{k=1}^n {k^3} = \big(\sum_{k=1}^n k\big)^2$ without induction
115460
Proving $a\mid b^2,\,b^2\mid a^3,\,a^3\mid b^4,\ldots\implies a=b$ - why is my approach incorrect
137010
What are integers $x$ and $n$ such as $ x^4+x^3+x^2+x+1 = n^2$?
5358
How to prove that 2017 divides $1^{2017}+2^{2017}+\dots+2017^{2017}$?
54355
$1+x+\ldots+x^n$ perfect square
120954
Prove that: $\sqrt[3]{a_1^3+ a_2^3 +\cdots+a_n^3} \le \sqrt{a_1^2 + a_2^2 +\cdots+a_n^2}$
1379
Summation of $n^2x^n$ terms
95643
Proving $\sum_{cyc} \sqrt{a^2+ab+b^2}\geq\sqrt 3$ when $a+b+c=3$
113593
How can I prove that $\frac{n^2}{x_1+x_2+\dots+x_n} \le \frac{1}{x_1}+ \frac{1}{x_2} +\dots+ \frac{1}{x_n}$?
28347
Prove that $\sqrt 2 + \sqrt 3$ is irrational
50050
A formula for the power sums: $1^n+2^n+\dotsc +k^n=\,$?
138894
Prove that if $3\mid(a^2+b^2)$,then $3\mid a$ and $ 3\mid b$
76635
Proof through combinatorial argument
34059
$(a^{2^n}+1,a^{2^m}+1)=1 or 2$
65648
Different ways to come up with $1+2+3+\cdots +n=\frac{n(n+1)}{2}$
12910
For the Fibonacci numbers, show for all $n$: $F_1^2+F_2^2+\dots+F_n^2=F_nF_{n+1}$
114506
Expansion of $(1+\sqrt{2})^n$