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Perfect Square To Divisibility By 56 (Posted on 2010-04-01) Difficulty: 4 of 5
N is a positive integer such that each of 3*N + 1 and 4*N + 1 is a perfect square.

Is N always divisible by 56?

If so, prove it. Otherwise, give a counterexample.

See The Solution Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: my bad Comment 14 of 14 |
(In reply to re: Does this explain why 7 is a factor of n? by Jer)

You're quite right. I should have said only that either both k and l are divisible by 7, or neither are.

I was thinking mainly in terms of the earlier comments on modular arithmetic, given the additional identity n=k-l, and some surmises of my own about squares that are the sum of consecutive squares while also being the difference between consecutive cubes.

I'll try not to wander in future!


  Posted by broll on 2010-04-06 15:32:36
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