Let a b be positive integers If b a and b a 2 prove that

Let a, b be positive integers. If b | a and b | (a + 2) prove that b = 1 or b = 2

Solution

Ans-

Given a,b are positive integers.b|a and b|(a+2).

to prove b=1 or b=2

proof-

Let a=x1b and (a+2)=x2b for some positive integers x1 and x2.

now (x1*b+2)=x2*b

or,(x2-x1)b=2 ,now if x2=1 and x1=1 then b=2 and if x2=4 and x1=2 then b=1

remember for positive integers