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Sum of squares of digits

Source: Brazilian MO, 2011, Problem 1

October 20, 2011
algebra unsolvedalgebra

Problem Statement

We call a number pal if it doesn't have a zero digit and the sum of the squares of the digits is a perfect square. For example, 122122 and 3434 are pal but 304304 and 1212 are not pal. Prove that there exists a pal number with nn digits, n>1n > 1.
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