MathDB

3

Part of 2012 International Zhautykov Olympiad

Problems(2)

P(Q(x)) + P(R(x))=constant => P(x) or Q(x)+R(x) is constant

Source: International Zhautykov Olympiad 2012 - D1 - P3

1/31/2012
Let P,Q,RP, Q,R be three polynomials with real coefficients such that P(Q(x))+P(R(x))=constantP(Q(x)) + P(R(x))=\text{constant} for all xx. Prove that P(x)=constantP(x)=\text{constant} or Q(x)+R(x)=constantQ(x)+R(x)=\text{constant} for all xx.
algebrapolynomialalgebra unsolved
All integer solutions of the equation 2x^2 - y^{14} = 1

Source: International Zhautykov Olympiad 2012 - D2 - P3

1/31/2012
Find all integer solutions of the equation the equation 2x2āˆ’y14=12x^2-y^{14}=1.
modular arithmeticnumber theorygreatest common divisorDiophantine equationnumber theory proposed