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Quadratic residues in a given interval

Source: Brazilian Math Olympiad, Problem 2

November 2, 2007

quadraticsmodular arithmeticinductionnumber theory unsolvednumber theory

Problem Statement

Find the number of integers

c

such that \minus{}2007 \leq c \leq 2007 and there exists an integer

x

such that x^2 \plus{} c is a multiple of

2^{2007}