Question

a+b=135
(a,b)=9
a=?
b=?

Answer 1

(a,b)=9⇒a=9k, b=9t  cu conditia ca (k,t)=1 (!)
a+b=135
9k+9t=135
9(k+t)=135
k+t=15, k,t ∈N*
Tinand cont si de prima relatie (!) obtinem:
(k,t)∈{(1,14):(2,13);(4,11);(7,8);(8,7);(11,4),(13,2);(14,1)}
Dupa ce facem toate calculele vom obtine:

S:(a,b)∈{(9,126);(18,117);(36,99);(63,72);(72,63);(99,36);(117,18);(126,9)}