Question

Determinati numerele a si b stiind ca : (a,b)=7 si a+b=28

Answer 1

Daca (a,b)=7 => 7 | a si 7 | b => a=7x si b=7y , cu x,y ∈N* si (x,y)=1.
a+b=35 => 7x+7y=35
7(x+y)=35
x+y=5
x=1=>y=4 => a=7 si b=28
x=2=>y=3 => a=14 si b=21
x=3=>y=2 => a=21 si b=14
x=4=>y=1 => a=28 si b=7
Solutie: (a,b)∈{(7,28};(14,21);(21,14);(28,7)}