MathDB

2

Part of 1990 Iran MO (2nd round)

Problems(2)

Solve (x^2-x)(x^2-2x+2)=y^2-1 [Iran Second Round 1990]

Source:

12/1/2010
Find all integer solutions to the equation (x2−x)(x2−2x+2)=y2−1(x^2-x)(x^2-2x+2)=y^2-1
number theory proposednumber theory
Nice roots problem [Iran Second Round 1990]

Source:

12/1/2010
Let α\alpha be a root of the equation x3−5x+3=0x^3-5x+3=0 and let f(x)f(x) be a polynomial with rational coefficients. Prove that if f(α)f(\alpha) be the root of equation above, then f(f(α))f(f(\alpha)) is a root, too.
algebrapolynomialquadraticsquadratic formulaalgebra proposed