6n^3 + 3 is not a perfect 6th power.

mathmaniac

Active member
Prove that the number 6n3 + 3 cannot be a perfect sixth power of
an integer for 'any natural number n.​3

mathbalarka

Well-known member
MHB Math Helper
Re: 6n^3+3 is not a perfect 6th power.

If we consider modulo 7, then 6n^3 + 7 is 2, 3 or 4 but 6-th powers of any integer are 0 or 1 modulo 7. Hence, QED.