The first few solutions to are , (7, 20), (751530, 1292054400) (OEIS A008849
and A048948) .... Lucas stated that there are
an infinite number of solutions (Dickson 2005, p. 56), but only solutions up
to the fourth are known to be complete.
The first few solutions to are , (43098, 1729), ... (OEIS A008850
and A048949), with only solutions up to the
second known to be complete.