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11... 122 ...25 is a perfect square

Source: 1981 Swedish Mathematical Competition p1

March 28, 2021
Perfect Squarenumber theory

Problem Statement

Let N=11⋯122⋯25N = 11\cdots 122 \cdots 25, where there are nn 11s and n+1n+1 22s. Show that NN is a perfect square.
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