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content/number-theory/ModLog.h

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* License: CC0
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* Source: own work
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* Description: Returns the smallest $x > 0$ s.t. $a^x = b \pmod m$, or
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* $-1$ if no such $x$ exists. Note that Modlog(a,1,m) can be used to
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* $-1$ if no such $x$ exists. modLog(a,1,m) can be used to
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* calculate the order of $a$.
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* Time: $O(\sqrt m)$
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* Status: tested for all 0 <= a,x < 500 and 0 < m < 500.
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* 1. b is divisible by p^x
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* 2. b is divisible only by some p^y, 0<y<x
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* 3. b is not divisible by p
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* The important thing to note is that in case 2, modLog(a,b,m) (if
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* it exists) cannot be > sqrt(m), (technically it cannot be >= log2(m)).
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* The important thing to note is that in case 2, modLog(a,b,m) (if
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* it exists) cannot be > sqrt(m), (technically it cannot be >= log2(m)).
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* So once all exponenents of a that are <= sqrt(m) has been checked, you
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* cannot have case 2. Case 2 is the only tricky case.
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*

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