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#### mathmaniac

##### Well-known member

- Mar 4, 2013

- 188

^{3}+ 3 cannot be a perfect sixth power of

an integer for 'any natural number n.

^{3}

- Thread starter mathmaniac
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- Thread starter
- #1

- Mar 4, 2013

- 188

an integer for 'any natural number n.

- Mar 22, 2013

- 573

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.