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Infinite Triplet and Perfect Square (Posted on 2015-08-16) Difficulty: 3 of 5
Does there exist an infinite number of positive integer triplets (x,y,z) with x < y < z such that:
x, y and z describe an arithmetic sequence, and:
Each of xy+1, yz+1 and zx+1 is a perfect square?

Give reasons for your answer.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

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more Sloane Comment 3 of 3 |
Considering the examples provided, the differences in the AP are 7,26,97,362,1351,... which looks to be

Edited on August 20, 2015, 9:24 am
  Posted by xdog on 2015-08-20 09:23:33

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