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-   -   An extension of NFS (https://www.mersenneforum.org/showthread.php?t=27426)

 RomanM 2021-12-22 13:59

An extension of NFS

Hi.
Both QS and NFS stuck with famouse A^2==B^2 mod p.
If we look on the A^3==B^3 mod p that do the split also (30% vs 50% for quadratic)
and in general to A^n==B^n*m & B^m=y mod p?? (1)
as a result, for n*m=2*3*5*7*11... the amount of (1) grow [B]outstanding[/B] fast.

It is necessary to assess and verify the possibility of applying this approach.
QS is not good i.e. (A+t)^n-p>>sqrt(p) for n>2 so this lead us to huge FB, long sieve and as result - very very tiny number of smoth numbers.

NFS in spite of this sieve the Linear (!!!) things ((a-b*m)&&(a-b*θ)), and sieve for different n*m is nor do not impossible, but likely not super hard.
LA will be harder, complicated and interesting, thought

Root of polynomial, root of m degree, m>=2.
We have a problem here...
How do You think, Is this idea viable or not?

 Dr Sardonicus 2021-12-22 14:06

[QUOTE=RomanM;595937]<snip>
How do You think, Is this idea viable or not?[/QUOTE]
Not.

 RomanM 2021-12-22 14:11

Ok. Thank You.