Journal of Integer Sequences, Vol. 16 (2013), Article 13.8.8 |

Department of Mathematics

University of Waikato

Private Bag 3105, Hamilton

New Zealand

**Abstract:**

We prove that the only solutions to the equation
with at most three distinct prime factors are 3, 35 and 1045.
Moreover, there exist at most a finite number of solutions to
with
,
and there are at most
2^{2k+k}-*k* squarefree solutions to
if
.
Lastly the number of solutions to
as
is
.

(Concerned with sequences A062699 A068390 A104901.)

Received June 13 2013; revised versions received August 4 2013;
September 19 2013; September 26 2013. Published in *Journal of
Integer Sequences*, October 13 2013.

Return to