New posts in problem-solving

IMO 2013 Problem 6

Proving that $T$:$(x_1,...,x_n) \rightarrow (\frac {x_1+x_2}{2},\frac {x_2+x_3}{2},...,\frac {x_n+x_1}{2})$ leads to nonintegral components

Find all the integer pairs $(x, y)$ which satisfy the equation $x^5-y^5=16xy$

Zombie Survival: What is the optimal way to place seven entities on an infinite grid to reduce number of adjacent pairs?

Proving a number defined by a sequence is a square number

What book would you recommend to significantly improve my problem solving skills?

book recommendation for problem-solving [closed]

Book recommendations for Problem Solving

If $m,n\in N$ Prove that there is such a positive integer k, such that $(\sqrt{m}+\sqrt{m+1})^n=\sqrt{k}+\sqrt{k+1}$

Problem-solving

Problem Solving Methods [duplicate]

Proving Holder's inequality using Jensen's inequality

How to suceed in mathematical olympiads and competitions?

Formula(s) for sharing multiple golden geese

Any partition of $\{1,2,\ldots,100\}$ into seven subsets yields a subset with numbers $a,b,c,d$ such that $a+b=c+d$. [closed]

Proving that $\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\dots+\frac{1}{\sqrt{100}}<20$

If $(n_k)$ is strictly increasing and $\lim_{n \to \infty} n_k^{1/2^k} = \infty$ show that $\sum_{k=1}^{\infty} 1/n_k$ is irrational

For any unbounded set of real numbers, is there a subset which almost coincides with a uniformly spread out set of points an infinite amount of times?

Soft question- The Bashing Technique and Other powerful techniques for Olympiads

Solutions to $a,\ b,\ c,\ \frac{a}{b}+\frac{b}{c}+\frac{c}{a},\ \frac{b}{a} + \frac{c}{b} + \frac{a}{c} \in \mathbb{Z}$