Found problems: 2
2008 Chile National Olympiad, 6
It is known that the number $\pi$ is transcendental, that is, it is not a root of any polynomial with integer coefficients. Using this fact, prove that the same is true for the number $\pi + \sqrt2$.
1984 Miklós Schweitzer, 4
[b]4.[/b] Let $x_1 , x_2 , y_1 , y_2 , z_1 , z_2 $ be transcendental numbers. Suppose that any 3 of them are algebraically independent, and among the 15 four-tuples on $\{x_1 , x_2 , y_1, y_2 \}$, $\{ x_1 , x_2 , z_1 , z_2 \} $ and $ \{y_1 , y_2 , z_1 , z_2 \} $ are algebraically dependent. Prove that there exists a transcendental number $t$ that depends algebraically on each of the pairs $\{ x_1 , x_2\}$ , $\{ y_1 , y_2 \}$, and $\{ z_1 , z_2 \}$. ([b]A.37[/b])
[L. Lovász]