# Math forum

 Sums of integers are squares Options
eigenein
 #1 Posted : Thursday, April 05, 2012 9:06:12 PM
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How can I find the set of positive integers S={a,b,c,d,e,f,g,h,i} such that:

1. a+bb+ca+c are squares,
2. d+ee+fd+f are squares,
3. g+hh+ig+i are squares,
4. a+b+c=d+e+f=g+h+i is square?

If there are several solutions then choose with minimal a+b+c.

Mike Poliquin
 #2 Posted : Thursday, May 03, 2012 5:39:05 AM
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a = 17, b = 32, c = 32, d = 17, e = 32, f = 32, g = 17, h = 32, i = 32

a + b = d + e = g + h = 49
b + c = e + f = h + i = 64
a + c = d + f = g + i = 49
a + b + c = d + e + f = g + h + i = 81

MP

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