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(x+1)^3 + (x + 2)^3 + (x + 3)^3 + (x + 4)^3 = (x + n)^3 diophantine

Source: Mathematics Regional Olympiad of Mexico Northeast 2018 P3

September 12, 2022
Diophantine equationnumber theory

Problem Statement

Find the smallest natural number nn for which there exists a natural number xx such that (x+1)3+(x+2)3+(x+3)3+(x+4)3=(x+n)3.(x+1)^3 + (x + 2)^3 + (x + 3)^3 + (x + 4)^3 = (x + n)^3.
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