Question

determinati numerele a si b,stiind ca (a,b)egal cu 7 si a+b egal cu 35

Answer 1

(a,b)=7

a=7x

b=7y

a+b=35

7x+7y=35

7(x+y)=35

x+y=5

(x,y)=1

1. x=1⇒ a=7

y=4⇒ b=28

2. x=2⇒ a=14

y=3⇒ b=21

3. x=3⇒ a=21

y=2⇒ b=14

4. x=4⇒ a=28

y=1⇒ b=7

(a,b)∈{(7,28),(14,21),(21,14),(28,7)}