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Old 2017-07-11, 05:42   #1
devarajkandadai
 
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May 2004

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

For purpose of this illustration I use the composite number 105=3*5*7
Algorithm for finding suitable bases in the ring of Gaussian integers.
a) In pari run the programme { is(n)=Mod(n,105)^104==1}
b) select(is,[1..100]); we now get several rational integer bases for pseudoprimality of 104. For purpose of this illustration I have selected 3 viz
8, 22 and 29. split 8 into two parts one real and the other imaginary such that each has two or three of the factors of 105- hence we get (15-6*I). Thisis a suitable base for
pseudoprimality of 105. Similarly we can split 22 into (15+7*I) and 29 into (14+15Î).
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