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2008 a fourth power? Baseless! (Posted on 2010-10-09) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

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Some Thoughts No Subject | Comment 1 of 3

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
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