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Old 2017-10-05, 04:54   #1
devarajkandadai
 
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May 2004

22·79 Posts
Default pari-algorithm for finding Gaussian integer bases

For finding rational integer bases for Fermat pseudoprimality of composite (square-free) composite numbers we need the following program in pari:
{is(n)=Mod(n,N)^(N-1)==1}
Next select(is,[1..1000])

However for finding Gaussian integer bases for the same we do not need pari.
Let N= m.r.p , say, where m, r and p are all prime. Then one of the combinations of
m,r and p,one at a time or two at a time, or definitely three at a time plus I works.Example - 105 = 3*5*7
Here 15+ 7*i , or 21 + 5*I will work; in any case 105 + I will work. Of course you need pari to verify.
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