Apr 1, 2013 Thread starter #1 mathmaniac Well-known member Mar 4, 2013 188 Prove that the number 6n3 + 3 cannot be a perfect sixth power of an integer for 'any natural number n.3
Prove that the number 6n3 + 3 cannot be a perfect sixth power of an integer for 'any natural number n.3
Apr 2, 2013 #2 mathbalarka Well-known member MHB Math Helper Mar 22, 2013 573 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.
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.