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Old 2017-09-23, 04:31   #1
devarajkandadai
 
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May 2004

31610 Posts
Default pari- p-adic numbers

We can use pari to create sequences similar to that on page 19 of Borevich and Shafarevich's book, number theory as follows:

Code: {is(n)=Mod(n,7)^2==2}
select(is,[1..100])
Next {is(n)=Mod(n,7^2)^2==2}
select(is,[1..1000])
next {is(n)=Mod(n,7^3)^2==2}
select(is,[1..1000])

You will get three sequences, the first of which corresponds to x_0.Second corresponds to x_1 and the third corresponds to x_2 of page 19 of the book.
Thus we get three sequences from which we can form a sequence conforming with 3.3 of the same. Needless to say this process can be continued.Important point: we have formed the required sequence without solving any linear equation.
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