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Bundeswettbewerb Mathematik 1977 Problem 2.3

Source: Bundeswettbewerb Mathematik 1977 Round 2

October 10, 2022

number theoryinfinitely many solutionsIntegersGeneralization

Problem Statement

Show that there are infinitely many positive integers

a

that cannot be written as

a = a_{1}^{6}+ a_{2}^{6} + \ldots + a_{7}^{6},

where the

a_i

are positive integers. State and prove a generalization.