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Consecutive Integers As Sum Of Square And Cube

Source: Bundeswettbewerb Mathematik 2017, Round 2 - #4

September 3, 2017

number theorysquarecube

Problem Statement

We call a positive integer heinersch if it can be written as the sum of a positive square and positive cube. Prove: There are infinitely many heinersch numbers

h

, such that

h-1

and

h+1

are also heinersch.

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