Suppose that 2M -N +N define a interval of square numbers, 2N wide.
The distance between the extremes a^2 & b^2 can be formulate as n^2+2an, (n=b-a), as they are squares numbers.
In other words
See that in the above expression:
[When ratio a/n decreases, the remainder of (a/a+n) is convergent to 0 and P -> na/8 (but never reaching it).
[When ratio n/a decreases, the remainder of (a/a+n) is convergent to 1 and P -> na/4 (never reaching).
For each value of "a" there is no integer any more under a certain ratio in the P expression (and same for "n").
So for the higher P values a~n
Only fits for a=4 P=3 which is the same solution posted by Brian.
Edited on January 21, 2016, 1:43 am
Posted by armando
on 2016-01-19 16:40:48