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Consecutive Contemplation (Posted on 2012-11-08) Difficulty: 3 of 5
Each of the n consecutive positive integers x+1, x+2, ...., x+n is expressible as the sum of squares of two distinct positive integers.

Determine the maximum value of n and prove that no higher value of n is possible.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts re: Not proven yet but I have a guess, AGREE | Comment 2 of 6 |
(In reply to Not proven yet but I have a guess by Jer)

Assuming that no two consecutive odd numbers are the sum of two distinct positive integers==> than 3 is the limit, i.e. even number S, THEN ODD S+1, then even again s+2.

To show that such a triple exist , show an example :

e.g. 800 (=400+400), 801 (=576+225), 802 (=441+361),

  Posted by Ady TZIDON on 2012-11-08 17:52:34
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