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Find minimum sum of A and B using given operations
By greedyman, 12 years ago, In English

You have positive numbers A and B (1 <= A,B <= 10^18) and following operations:
  1) If P is prime number and divides A and B, then A/=P and B/=P.
  2) If P is prime number and divides A and P^2 divides B, then A/=P and B/=P^2.
Find minimum sum of A and B using operations 1 and 2 (no matter how many times).

Do you have any ideas?
It seems to have quite easy solution, and should work in something like O(lg max(A,B)).

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12 years ago, hide # |
 
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I think that this problem can be solved next way:

  1. g1 = gcd(A, B), B /= g1 — remove common prime divisors
  2. g2 = gcd(A, B), A /= g1, B /= g2 — remove common prime divisors, that were twice at B
  3. res = A + B
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