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Forum: Abstract Algebra & Algebraic Number Theory 2017-01-20, 21:12
Replies: 13
Views: 9,245
Posted By Till
This is not about my original question, but at...

This is not about my original question,
but at least I found a nice approach to solve for t in t^2 == N (mod p^e), for any e>=2.
Look at the comment of Gottfried Barthel here:...
Forum: Abstract Algebra & Algebraic Number Theory 2016-01-13, 19:22
Replies: 13
Views: 9,245
Posted By Till
Hi, your answer looks substantial. I agree...

Hi,
your answer looks substantial.

I agree with "NP-complete" since I already found out in this thread
"finding square roots modulo composite numbers is a computational problem equivalent to...
Forum: Abstract Algebra & Algebraic Number Theory 2016-01-13, 15:27
Replies: 13
Views: 9,245
Posted By Till
What you describe now is just a faster variant...

What you describe now is just a faster variant of the formula I started with. Both variants require g to be prime, or am I wrong on that?

My question was if there is an efficient solution even...
Forum: Abstract Algebra & Algebraic Number Theory 2016-01-13, 11:50
Replies: 13
Views: 9,245
Posted By Till
Tonelli-Shanks does not apply here because the...

Tonelli-Shanks does not apply here because the modulus g^2 is not prime.
The formula in Pomerance's paper works at least for a modulus g^2, g prime.

But it was good that you put my nose to the...
Forum: Abstract Algebra & Algebraic Number Theory 2016-01-13, 09:34
Replies: 13
Views: 9,245
Posted By Till
Aah :) Good thing, your counterexample. It...

Aah :)

Good thing, your counterexample.
It is said in the paper that g should be prime. One of the things I wanted to know is if that is really necessary. Your counterexample tells me that it is....
Forum: Abstract Algebra & Algebraic Number Theory 2016-01-13, 09:23
Replies: 13
Views: 9,245
Posted By Till
Hi, thanks for the quick reply! I think I...

Hi,
thanks for the quick reply!

I think I copied everything correctly.

g is Pomerance's analog of the q-parameter in Contini's thesis; g^2 is the a-parameter.

Maybe there is another...
Forum: Abstract Algebra & Algebraic Number Theory 2016-01-13, 08:05
Replies: 13
Views: 9,245
Posted By Till
MPQS b-parameter and Pell-like equations

The b-parameter in MPQS, following [Pomerance 1985: "The quadratic sieve algorithm"],
is defined as

b^2 == N (mod g^2) .......................(1)

and has...
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