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: 4

2021 Science ON grade VII, 3
Tags: inequality , newton sums , symmetric sums , algebra
Are there any real numbers $a,b,c$ such that $a+b+c=6$, $ab+bc+ca=9$ and $a^4+b^4+c^4=260$? What about if we let $a^4+b^4+c^4=210$? [i] (Andrei Bâra)[/i]

2021 Science ON grade X, 3
Tags: complex number , newton sums , vieta , algebra
Consider a real number $a$ that satisfies $a=(a-1)^3$. Prove that there exists an integer $N$ that satisfies $$|a^{2021}-N|<2^{-1000}.$$ [i] (Vlad Robu) [/i]

2021 Science ON all problems, 3
Tags: complex number , newton sums , vieta , algebra
Consider a real number $a$ that satisfies $a=(a-1)^3$. Prove that there exists an integer $N$ that satisfies $$|a^{2021}-N|<2^{-1000}.$$ [i] (Vlad Robu) [/i]

2021 Science ON all problems, 3
Tags: algebra , inequality , symmetric sums , newton sums
Are there any real numbers $a,b,c$ such that $a+b+c=6$, $ab+bc+ca=9$ and $a^4+b^4+c^4=260$? What about if we let $a^4+b^4+c^4=210$? [i] (Andrei Bâra)[/i]