Divisors of Sum and Difference of Two Relativel Prime Numbers
\[gcd(a,b)=1\]
then \[gcd(a+b,a-b)=1 \; or \; 2\]
.Suppose
\[d\]
divides \[a+b\]
and \[a-b\]
so \[d\]
divides \[(a+b)+(a-b)=2a\]
and \[d\]
divides \[(a+b)-(a-b)=2b\]
hence \[d\]
divides 2 or \[d\]
divides \[gcd(a,b)=1\]
. 
