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TOT 533 1997 Spring J A5 1997^{17} not sum of perfect squares

Source:

September 11, 2024
number theoryperfect cubeconsecutive

Problem Statement

Prove that the number
(a) 979797^{97}
(b) 1997171997^{17}
cannot be equal to a sum of cubes of several consecutive integers.
(AA Egorov)