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

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Found problems: 27

2006 Pan African, 2
Tags: Vieta , algebra , polynomial , Rational Root Theorem , number theory unsolved , number theory
Let $a, b, c$ be three non-zero integers. It is known that the sums $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}$ and $\frac{b}{a}+\frac{c}{b}+\frac{a}{c}$ are integers. Find these sums.

1995 Vietnam Team Selection Test, 2
Tags: algebra , polynomial , modular arithmetic , search , Rational Root Theorem , algebra unsolved
Find all integers $ k$ such that for infinitely many integers $ n \ge 3$ the polynomial \[ P(x) =x^{n+ 1}+ kx^n - 870x^2 + 1945x + 1995\] can be reduced into two polynomials with integer coefficients.