{75, 100, 125} is an example of an arithmetic progression of positive integers such that the nth term is a perfect nth power.
Find a longer sequence with this feature.
What is the longest you can get?
P.S. Trival solution(d=0) excluded.
(In reply to
Further conditions? by ed bottemiller)
I agree. It is not required by the question that each term be a perfect nth power, only the nth. Hence I computed that the 47th term of the sequence
84,302,701,379,661,926,579,709,743,177,268,059,889,094,454,377,047,954,731,354,904,953,935,200,516,327d + 5,477,161,311,821 is 47^47; with n,d, and a1 all prime.
However I shall also give thought to Justin's version which presents more of a challenge.
Edited on July 22, 2010, 4:08 pm

Posted by broll
on 20100722 16:04:54 