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\sqrt{1 + 12n^2} in N => 2 + 2\sqrt{1 + 12n^2} = m^2

Source: 2008 Dutch IMO TST P4

January 10, 2020
Perfect Squarenumber theoryradical

Problem Statement

Let nn be positive integer such that 1+12n2\sqrt{1 + 12n^2} is an integer. Prove that 2+21+12n22 + 2\sqrt{1 + 12n^2} is the square of an integer.
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