Can the base B number 2008 be a perfect fourth power, where B is a positive integer ≥ 9?

If so, give an example. If not, prove that the base B number 2008 can never be a perfect fourth power.

2008 in base B means a number which can be written as

B^3 + 8, this should equal x^4.

Putting B = 9, 10, 11, 12, 13 there is no solution for x. But cannot see a pattern or generalise.

This also means x^4 - B^3 - 8 = 0 which is a complex eqn.

Posted by Vishal Gupta on 2010-10-09 15:52:13