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Search: Posts Made By: Dr Sardonicus
Forum: Number Theory Discussion Group 2020-11-03, 13:58
Replies: 12
Views: 3,445
Posted By Dr Sardonicus
I am unaware of any such method. For primes...

I am unaware of any such method.

For primes p congruent to 1 (mod 4) I don't know of any faster way than factoring x2 - r over the finite field with p elements. In Pari-GP sqrt(Mod(r, p)) will...
Forum: Number Theory Discussion Group 2020-11-01, 21:22
Replies: 12
Views: 3,445
Posted By Dr Sardonicus
How do you calculate the mapping function...

How do you calculate the mapping function ?[/QUOTE]
Very simple: 11 and -11 are the square roots of -1 (mod 61).

The fact that 61R = P1P2 has consequences. Typically*, a square Mod(a,61) +...
Forum: Number Theory Discussion Group 2020-11-01, 15:52
Replies: 12
Views: 3,445
Posted By Dr Sardonicus
Then you are arguing with a definition. First,...

Then you are arguing with a definition. First, an ideal M in a commutative ring R is a subset of R which is

(a) closed under addition (if x and y are in M then so is x + y),

and

(b) closed...
Forum: Number Theory Discussion Group 2020-11-01, 02:58
Replies: 12
Views: 3,445
Posted By Dr Sardonicus
Pari-GP begs to differ: ?...

Pari-GP begs to differ:

? (Mod(13,61)+Mod(25,61)*I)^30

%1 = Mod(60, 61)

which is -1 (mod 61). You appear to have interchanged real and imaginary parts, which is equivalent to taking the...
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