MathDB

1

Part of 2007 Poland - Second Round

Problems(2)

Polish MO 2007 Second Round Day 1, problem 1

Source:

2/28/2007
Polynomial P(x)P(x) has integer coefficients. Prove, that if polynomials P(x)P(x) and P(P(P(x)))P(P(P(x))) have common real root, they also have a common integer root.
algebrapolynomial
Polish MO 2007 Second Round Day 2, problem 1

Source:

2/28/2007
aa, bb, cc, dd are positive integers and ad=b2+bc+c2ad=b^{2}+bc+c^{2} Prove that a2+b2+c2+d2a^{2}+b^{2}+c^{2}+d^{2} is a composed number.