MathDB

14

Part of 1991 IMO Shortlist

Problems(1)

f(x) = ax^2 + bx + c is a perfect square for 2p - 1 integers

Source: IMO ShortList 1991, Problem 14 (POL 3)

8/15/2008
Let a,b,c a, b, c be integers and p p an odd prime number. Prove that if f(x) \equal{} ax^2 \plus{} bx \plus{} c is a perfect square for 2p \minus{} 1 consecutive integer values of x, x, then p p divides b^2 \minus{} 4ac.
modular arithmeticnumber theoryquadraticsPerfect SquareDiscriminantIMO Shortlist