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299..98200..0029 = sum of squares of 3 consecutive naturals

Source: Mathematics Regional Olympiad of Mexico Center Zone 2009 P4

November 10, 2021
Perfect SquarePerfect SquaresconsecutiveDigitsnumber theory

Problem Statement

Let N=2  99…9⏟n  times  82  00…0⏟n  times  29N = 2 \: \: \underbrace {99… 9} _{n \,\,\text {times}} \: \: 82 \: \: \underbrace {00… 0} _{n \,\, \text {times} } \: \: 29. Prove that NN can be written as the sum of the squares of 33 consecutive natural numbers.
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