Ariel Pacetti on Tue, 16 Sep 2003 23:54:12 -0500 (CDT) |
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Re: gcd of Modded integers |
No because the congruence equations are equivalence clase. Look at this: since (9,26)=1, there is an element in the same equivalence class as 9 but not divisible by 3 (for example 35 = 9 + 26). Then 3 is not a divisor of the equivalence class. A congruence number (i.e. a number Mod(a,b)) will have a non-trivial divisor if and only if the gcd(a,b) is different from 1. For example: gcd(Mod(3,18),Mod(9,18))= Mod(3,18) Ariel On Tue, 16 Sep 2003, Manish wrote: > I came across this on my GP/PARI Version 2.1.5. > > shouldnt I expect gcd to be Mod(3,26) > > > ? gcd(Mod(9,26), Mod(3,26)) > %1 = Mod(1, 26) > > > thanks > Manish >