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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)

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Once more into the fray... | Comment 4 of 14 |

The third value I find which satisfies the conditions is:

2118480 (=37830 * 56)

6355441 (= 3*2118480 + 1 = 2521 squared)

8473921 (= 4*2118480 + 1 = 2911 squared)

Tested N up to 10,000,000

 


  Posted by ed bottemiller on 2010-04-01 16:06:15
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