GCD(a+h,b+k) - Formula Given GCD(a,b) & GCD(h,k)?

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SUMMARY

No formula exists for calculating gcd(a+h, b+k) based on the values of gcd(a, b) and gcd(h, k). The discussion highlights that even when gcd(a, b) and gcd(h, k) are both equal to 1, the results for gcd(a+h, b+k) can vary significantly. For example, with (a, b, h, k) = (1, 1, 1, 1), gcd(a+h, b+k) equals 2, while with (1, 2, 2, 1), it equals 3. This demonstrates the lack of a consistent relationship between these gcd values.

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harshant
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Is there a formula for gcd(a+h,b+k) given gcd(a,b) and gcd(h,k)?...jus wondering
 
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harshant said:
Is there a formula for gcd(a+h,b+k) given gcd(a,b) and gcd(h,k)?...jus wondering
No such formula exists
 
ramsey2879 said:
No such formula exists

Yes, there can't be such a formula. For (a, b, h, k) = (1, 1, 1, 1) and (1, 2, 2, 1), gcd(a, b) = gcd(h, k) = 1, but gcd(a+h, b+k) is 2 and 3 (respectively).
 

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