- #1

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## Homework Statement

Show that gcd(a+b,a-b) is either 1 or 2. (hint, show that d|2a and d|2b)

## Homework Equations

d = x(a+b)+y(a-b)

## The Attempt at a Solution

so by the definition of divisibility:

a+b = dr

a-b = ds

adding and subtracting these equalities from eachother we can arrive at where the hint wanted us to conclude:

(r+s) = 2a/d

(r-s) = 2b/d

Trying to figure out what to do from here, having a hard time using the hint to restrict d to 1 or 2.