2

Part of 1995 Irish Math Olympiad

Problems(2)

infinitely many solutions

Source: Ireland 1995

Determine all integers

a

for which the equation x^2\plus{}axy\plus{}y^2\equal{}1 has infinitely many distinct integer solutions

x,y

Diophantine equationnumber theory proposednumber theory

complex numbers

Source: Ireland 1995

a,b,c

be complex numbers. Prove that if all the roots of the equation x^3\plus{}ax^2\plus{}bx\plus{}c\equal{}0 are of module

1

, then so are the roots of the equation x^3\plus{}|a|x^2\plus{}|b|x\plus{}|c|\equal{}0.

abstract algebratrigonometryalgebra unsolvedalgebra