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.
(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