MathDB
A very nice problem IMO LongList 1992 ROM2

Source:

September 2, 2010
modular arithmeticquadraticsnumber theoryDivisibilityIMO ShortlistIMO Longlist

Problem Statement

Let aa and bb be integers. Prove that 2a2−1b2+2\frac{2a^2-1}{b^2+2} is not an integer.
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