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.

AND
OR
NO

Found problems: 102

2015 Poland - Second Round, 1
Real numbers $x_1, x_2, x_3, x_4$ are roots of the fourth degree polynomial $W (x)$ with integer coefficients. Prove that if $x_3 + x_4$ is a rational number and $x_3x_4$ is a irrational number, then $x_1 + x_2 = x_3 + x_4$.
rational irrational number polynomial sum algebra polynomials

2018 District Olympiad, 1
Show that $$\sqrt{n + \left[ \sqrt{n} +\frac12\right]}$$ is an irrational number, for every positive integer $n$.
irrational number algebra number theory