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$modinv identifier - mIRC
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$modinv returns the Multiplicative Modular Inverse for an integer.
Details
For integers (A,M) the Multiplicative Modular Inverse is a non-negative integer B less than M, which when multiplied by 'A' is 1 greater than a multiple of M. The modular inverse has a relationship with the $gcd where positive integers A and M can have $gcd(A,M) greater than 1, or there can be $modinv(A,M). But you cannot have both and you cannot have neither. The result of $modinv(A,M) is the same as $powmod(A,-1,M)
Synopsis
$modinv(N,modulus)
Returns -1 if no inverse exists
Parameters
- N - Integer
- modulus - divisor used for obtaining the inverse of N
Properties
None
Example
//var -s %rand $rand(1,2016) | echo -a the mod inverse ( %rand ,2017) is $modinv(%rand,2017) because $calc( ($modinv( %rand ,2017) * %rand) % 2017 ) is 1 Note: modinv(1,2017) = 1 because (1 * 1) is greater than (0*2017) //var %i 9 | var %a $rand(1,999) , %m $rand(1,999) | if ($gcd(%a,%m) > 1) echo 4 -a GCD( %a , %m ) = $v1 is greater than 1, so there is no mod inv(A,M): $modinv(%A,%M) | else echo 3 -a GCD( %A , %M ) = $gcd(%a,%m) so there is a mod inverse (A,M) and it is $modinv(%a,%m)
Compatibility
Added: mIRC v7.72
Added on: 27 Nov 2022
Note: Unless otherwise stated, this was the date of original functionality.
Further enhancements may have been made in later versions.