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.

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