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20(11) a tenth power? Baseless! (Posted on 2011-02-26) Difficulty: 3 of 5
Can the base N number 20B be a perfect tenth power, where N is a positive integer ≥ 12?

If so, give an example. If not, prove that the base N number 20B can never be a perfect tenth power.

No Solution Yet Submitted by K Sengupta    
Rating: 3.5000 (2 votes)

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possible solution Comment 1 of 1

Assume that it can.

Then 20B=x^10=(x^5)^2=p^2, where p^2=2N^2+11 in base N; but 11==3, mod8, hence the answer is 'no'.

Edited on February 27, 2011, 6:35 am
  Posted by broll on 2011-02-27 02:21:28

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