MathDB

1

Part of 1993 Kurschak Competition

Problems(1)

Square values of f(x)=ax^2+b

Source: Kürschák 1993, problem 1

7/20/2014
Let aa and bb be positive integers. Prove that the numbers an2+ban^2+b and a(n+1)2+ba(n+1)^2+b are both perfect squares only for finitely many integers nn.
inequalitiesquadraticsalgebranumber theory unsolvednumber theory