Notice that and

MATHEMATICS · Subjective · ICSE · Mathematics · Playing with Numbers · Playing with Numbers

Problem

Notice that

11 - 2 = 9 = 3^2

and

1111 - 22 = 1089 = 33^2

. Show that

\underbrace{(111111\dots 1)}_{2n \text{ lots of 1}} - \underbrace{(22222\dots 2)}_{n \text{ lots of 2}}

is a perfect square.

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