By subtracting 1 from the positive base N integer having the form XYXYXYZY, we get a perfect square. It is known that each of X, Y and Z represents a different base N digit from 0 to N-1, and X is nonzero.
What are the integer value(s) of N, with 3 ≤ N ≤ 16 for which this is possible?
(In reply to general solution (no proof yet)
I made a slight mistake in my initial attempt at a proof, so here is the proof.
if x=n-2 y=2 and z=0 then
thus x=n-2 y=2 and z=0 always gives a square plus 1
Posted by Daniel
on 2009-06-24 20:15:49