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Part of 2008 Junior Balkan Team Selection Tests - Moldova

Problems(1)

Source: Moldova Junior TST 2008 Day 2 Problem 1

Find all natural pairs

(x,y)

x

y

are relative prime and satisfy equality: 2x^2 \plus{} 5xy \plus{} 3y^2 \equal{} 41x \plus{} 62y \plus{} 21.

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