Mobius inversion brush title record
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2019-09-27 05:05:09
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BZOJ1101: [POI2007]Zap
- The meaning of problems: for given integers a, b and d, to find the number of positive integers x, y, satisfies x <= a, y <= b, and gcd (x, y) = d
- Request directly to the number of positive integers x, y, gcd (x, y) = d more difficult to find, and inquired about 50,000,
\ begin {gather *}
claim \ \ \ \ \ \ \ \ f (n) = \ \ sum \ nolimits ^ {\ b} _ {\ y = 1} \ \ \ sum \ nolimits ^ {\ a} _ { \. 1} X = \ [\ GCD (X, Y) = n-\] \\
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is \ \ \ \ \ \ \ \ \ \ \ F (n) = \ sum \ nolimits ^ {\ b} _ { \ = Y. 1} \ SUM \ NoLimits ^ {\ {A} _ \. 1} X = \ SUM \ NoLimits _ {\ n-| GCD (X, Y)} \. 1 \\
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as \ \ \ \ \ \ \ \ SUM \ NoLimits _ {\ n-| GCD (X, Y). 1} = \ SUM \ NoLimits _ {\ n-| D} \ [\ GCD (X, Y) = D \] \\
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F. (n- ) \ = \ \ SUM \ NoLimits _ {\ n-|} D \ \ F (D) \\
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then is hot Mobius inversion \\
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\ End Gather *} {
- Code:
Origin www.cnblogs.com/jiecaoer/p/11586397.html