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Part of 2005 France Team Selection Test

Problems(1)

Perfect square

Source: French TST 2005 - pb 1

5/26/2005
Let xx, yy be two positive integers such that 3x2+x=4y2+y\displaystyle 3x^2+x=4y^2+y. Prove that xāˆ’yx-y is a perfect square.
number theory unsolvednumber theory