Question

Aflati perechile de numere in care satisfac conditiile au suma 1089 si c.m.m.d.c al lor este 121

Answer 1

a + b = 1089
(a,b) = 121 ⇒ 121 y = a; 121 x = b
121 y + 121 x = 1089
121 ×(y+x) = 1089 ⇒ x+y = 9
(y,x) ∈ {(1,8);(8,1);(2,7);(7,2);(3,6);(6,3);(5,4);(4,5)}
→ a ∈ { 121, 968, 242, 847, 363, 726, 605, 484}
→ b ∈ { 121, 968, 242, 847, 363, 726, 605, 484}
Unde a ≠ b