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

[mathmaniac]

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

 

[mathbalarka]

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.