perplexus.info :: Just Math : Square pairs

Square pairs (Posted on 2018-02-07)

Let's denote by p(n) the greatest square less than or equal to n,
n being a positive integer.

List all pairs (m,n), for which:(2m+1)*p(2n+1) = 400; m being less than n.

See The Solution Submitted by Ady TZIDON

Rating: 5.0000 (1 votes)

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solution/spoiler

| Comment 2 of 3 |

(2m+1) is an odd factor of 400.

When (2m+1)=1, p(2n+1)=400 for n=200-219 inclusive with m=0.

When (2m+1)=5, p(2n+1)=80 which is not a square.

When (2m+1)=25, p(2n+1)=16 for n=8-11 inclusive with m=12.

That makes 24 pairs.

Posted by xdog on 2018-02-07 20:50:38

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