(I) Determine all possible values of a base-10 positive integer x such that:
sod(x²) - x = 2, where sod(n) denotes the sum of the digits in the base-10 representation of n.

(II) Determine all possible values of a base-11 positive integer y such that:
sod(y²) - y = 2, where sod(n) denotes the sum of the digits in the base-11 representation of n.

In each of (I) and (II) prove that these are the only respective valid value(s) corresponding to x and y.

By observation i found that 2, 5, 8, 14, 17 satisfy the first part.

Higher values dont as the sum of digits increases by only a few and number increases by a lot. Cant prove it though.

EDIT: 2, 4, 7, 9 will satisfy part 2.

Edited on September 27, 2010, 4:07 pm

Posted by Vishal Gupta on 2010-09-27 16:04:13