This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 3

2009 Federal Competition For Advanced Students, P1, 1
Tags: inequalities , factorial , exponential , exponential inequality , diophantine , induction , algebra
Show that for all positive integer $n$ the following inequality holds $3^{n^2} > (n!)^4$ .

2015 Balkan MO Shortlist, A5
Tags: algebra , inequalities , exponential inequality , exponential , exponential equation
Let $m, n$ be positive integers and $a, b$ positive real numbers different from $1$ such thath $m > n$ and $$\frac{a^{m+1}-1}{a^m-1} = \frac{b^{n+1}-1}{b^n-1} = c$$. Prove that $a^m c^n > b^n c^{m}$ (Turkey)

2010 Belarus Team Selection Test, 7.3
Tags: algebra , inequalities , exponential inequality , exponential
Prove that all positive real $x, y, z$ satisfy the inequality $x^y + y^z + z^x > 1$. (D. Bazylev)