perplexus.info :: Just Math : Numerator Divisibility Nuance

Numerator Divisibility Nuance (Posted on 2011-01-22)

Each of p and q is a positive integer, with p and q being relatively prime, such that:

p/q = 1 - 1/2 + 1/3 - 1/4 + ...... - 1/1318 + 1/1319

Prove that p is divisible by 1979.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

Not obvious to me

| Comment 2 of 4 |

Well, by combining adjacent pairs of terms, we can get

p/q = 1/2 + 1/12 + 1/30 + ...

1 - 1/6 - 1/20 - 1/42 - ...

But I don't see how this helps. Hope somebody makes progress on the analytic front.

Posted by Steve Herman on 2011-01-23 14:24:43

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