If I have the prime factors of two coprimes $a$ and $b$, is it possible to find the prime factors of $a + b$ and $a - b$ faster than a full factorization?
2026-03-31 17:20:14.1774977614
Factorization of sum and difference of factorized coprimes
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Yes. a+b and a-b are each co-prime to each of a and b. Therefore, you know that none of the prime factors of a or b is a factor of a+b or a-b. Therefore, there is no need to test a+b or a-b for those factors.