SOLUTION: What is the greatest proper fraction whose sum and product of the numerator & denominator are both perfect squares?

Question 1120699: What is the greatest proper fraction whose sum and product of the numerator & denominator are both perfect squares?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
What is the greatest proper fraction whose sum and product of the numerator & denominator are both perfect squares?
:
I came up with ,
Sum = 841, 29^2
product = 176400, 420^2
:
I may have cheated, I used a simple Basic program to find all the numerator/denominator pairs up to 1000 and found the one with the greatest decimal value
:
The basic program:
10 print "Find the greatest proper fraction where both the product and the sum are perfect squares": Print
15 Print "Numerator Denominator sum product decimal value"
20 for n = 1 to 1000
25 for d = 2 to 1000
27 if n = d then 60
28 if n > d then 60
30 a = n*d
35 b = SQR(a)
37 If b = int(b) then 40 else 60
40 c = n+d
50 e = SQR(c)
52 if e = int(e) then print n, d, a, c, n/d
60 next d
70 next n
80 end

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