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POWER CHAIN. (Posted on 2010-07-22) Difficulty: 4 of 5
{75, 100, 125} is an example of an arithmetic progression of positive integers such that the n-th term is a perfect n-th power.
Find a longer sequence with this feature.

What is the longest you can get?
P.S. Trival solution(d=0) excluded.

No Solution Yet Submitted by Ady TZIDON    
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Comments: ( Back to comment list | You must be logged in to post comments.)
re: Further conditions? | Comment 4 of 6 |
(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 2010-07-22 16:04:54

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