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Placing 4 integers within a set interval (Posted on 2017-02-17) Difficulty: 4 of 5
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

No Solution Yet Submitted by Ady TZIDON    
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re: Is this the idea? | Comment 2 of 4 |
(In reply to Is this the idea? by broll)

I agree that that us the idea.  Also,


1 < 7/4 < 8/1 < 9

where 

s=1 r=8, q=4, p=7, a = 1, b=9.

The challenge, of course, is to come up with a method for finding a satisfying p,q,r,s for any a and b, and particularly for a and b arbitrarily close.  Or at least, to prove that these always exist.





  Posted by Steve Herman on 2017-02-19 20:40:51
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