Question

Daca a+b=56 si (a,b)=8,atunci perechile (a,b) sunt....

Answer 1

(a;b)=8 ⇒ a=8m, b=8n 
a+b=8(m+n)=56
m+n=7
m=1, n=6, a=8, b=48
m=2, n=5, a=16, b=40
m=3, n=4, a=24, b=32
m=4, n=3, a= 32, b=24
m=5, n=2, a=40, b=16
m=6, n=1, a=48, b=8
corecteaza daca s-a scapat ceva.

Answer 2

daca (a;b)=8 inseamna ca a=8x si b=8y  unde (x;y) = 1
inlocuim ... => 8x+8y= 56  adica:  x+y= 7 = 1+6 = 2+5 = 3+4 ...
     
          =>  (a;b) = {(8;48):(16;40):(24;32):(32;24):(40;16);(48;8)}