The actual factorisation matters little to me; I would just like to be given hints / ideas on how to go about doing this kind of probem.
32.
I don't see how knowing the prime factorisation of 33 would help .-- talk ) 15 : 16, 28 October 2008 ( UTC)
33.
There are various techniques you can use-I would use factorisation for that one .-- talk ) 01 : 19, 27 March 2008 ( UTC)
34.
After that, he moved into the areas of Jordan algebras, Lie division rings, skew fields, free ideal rings and non-commutative unique factorisation domains.
35.
The quantum computer is capable of exponential speed ups on current classical algorithms for prime factorisation of numbers, however if this requires an exponentially large setup then our advantage is lost.
36.
Since any common factors of and are present in the factorisation of = =, it is recommended that and have only very small common factors, if any besides the necessary 2.
37.
He has been an active developer of the GMP-ECM implementation of the elliptic curve method for integer factorisation and of MPFR, an arbitrary precision floating point library with correct rounding.
38.
:Unique factorisation was, I think, thought to extend to quadratic integers, such that it was taken for granted and used in other proofs ( which were therefore false ).
39.
This requires knowing whether " t " is a quadratic residue modulo " N ", and there are no known methods for doing this without knowledge of the factorisation.
40.
It is not possible to tell whether \ mathbb Z / N \ mathbb Z [ \ sqrt t ] is actually a quadratic extension of " N " without knowing the factorisation.
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