Talk:UVa 106 - Fermat vs. Pythagoras

9^2+12^2=15^2 Who can tell me r=? & s=? in this case? Thanks.

[roticv] 9^2+12^2=15^2

is the same as

3^2 ( 3^2 + 4^2 = 5^2) in the case 3^2 + 4^2 = 5^2 r = 2, s = 1 [/roticv]

x,y,z are relative prime iff r,s are relative prime?
For r=5, s=3:

x = 5*5-3*3 = 16

y = 2*5*3 = 30

z = 5*5+3*3 = 34

r and s are relatively prime, but not x,y and z.

My maths is bad so I wonder if there is something wrong in the above example?

Re:Had you noticed this sentence:"one and only one of r,s is even number"

divisible by 2, but not by 4?
"This implies that one, but not both, of x,y must be even. (Otherwise, z would be divisible by 2, but not by 4)"

what's the point in this comment? :S