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Prove that 111...11222...225 is a perfect square

Source: 0

October 30, 2005
inductionPerfect Square

Problem Statement

Prove that the number 111…11⏟199722…22⏟19985\underbrace{111\ldots 11}_{1997}\underbrace{22\ldots 22}_{1998}5 (which has 1997 of 1-s and 1998 of 2-s) is a perfect square.
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