perplexus.info :: Just Math : Summing consecutive factorials

Summing consecutive factorials (Posted on 2018-06-26)

1!=1^2; 1!+2!+3!=3^2
Are there any other sums of n consecutive factorials that sum up to a perfect square?

Either list them all or prove there are none.

No Solution Yet Submitted by Ady TZIDON

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re(3): If you don't have to start with 1 ...

| Comment 5 of 7 |

Daniel, the square of any integer n=2 mod7 = 4 mod7.

For n=51 = 2 mod7, 51^2 = 2601 = 4 mod7

Posted by xdog on 2018-06-26 12:19:17

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