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Hi MathCentral I have this one proof that I almost get but am not quite how to go about doing it . I don't know how to ask this question. QUESTION: Let a and b integer and relatively prime. Proof that: GCD (a + b , a^{2}  ab + b^{2}) = 1 or 3 regards Carol 

Hi Carol, Suppose that d > 1 and d divides a + b and a^{2}  ab + b^{2}. Since gcd(a,b) = 1, either d does not divide a or d does not divide b. Suppose that d does not divide a. Write
Since d divides a + b, d divides 3ab. If d divides b then, since d divides a + b, d divides a. Thus d does not divide a or b so d divides 3. Thus d = 3. Penny 

