Question

(x,2y)=13 si x+2y=91 cat sunt x,y?

Answer 1

x=13k, k impar
2y=13l, l par
13k+13l=91
k+l= 7
daca k=1, l=6, x=13, y=39
daca k=3, l=4, x=39, y=26
daca k=5, l=2, x=13*5=65, y=13

O seara buna!

Answer 2

x+2y=91
(x,2y)=13 deci cmmdc(x,2y)=13
x =13a      2y =13b   ⇒ b = nr. par

13a+13b = 91
⇒ 13(a+b) = 91
⇒  a+ b = 7
deci pot fi perechile (1,6); (2,5), (3,4)
a = 1    b = 6      x = 13   2y = 13×6=78⇒ y = 39
a = 3    b = 4      x = 39    2y = 13×4=52⇒ y = 26
a = 5    b = 2      x = 65    2y = 13×2=26⇒y = 13