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Part of 2006 Team Selection Test For CSMO

Problems(1)

Xvii cono sur - peru tst 2006.

Source: Spanish Communities

Find all the pairs of positive numbers such that the last digit of their sum is 3, their difference is a primer number and their product is a perfect square.

LaTeXmodular arithmeticquadraticsnumber theoryrelatively primealgebradifference of squares