Given 2 real numbers a & b, b>a.
Find four distinct integers p,q,r, and s, complying with:
p^2 + q^2 = r^2 + s^2
a < p/q < r/s < b
(In reply to
re: Is this the idea? by Steve Herman)
I'm afraid I still don't really 'see' it.
One easy way to get solutions with a lot of variation is to choose a number like, say, 2576450045 = 5×13×17×29×37×41×53.
For obvious reasons this has 64 solutions ranging from {{1342, 50741}, {1451, 50738}, to {35398, 36379}, {35579, 36202}}: giving equally:
a<1342/50471<1451/50738<b (difference 0.002)
a<35398/36379< 35579/36202<b (difference 0.009)
That arbitrarily large differences can exist is plainly trivial.
Have I 'solved' the problem?  without some further constraint, I simply can't tell.

Posted by broll
on 20170220 00:52:17 