mersenneforum.org  

Go Back   mersenneforum.org > Great Internet Mersenne Prime Search > Math > Number Theory Discussion Group

Reply
 
Thread Tools
Old 2021-01-05, 01:42   #1
bhelmes
 
bhelmes's Avatar
 
Mar 2016

22×89 Posts
Default special quadratic polynomials : f(n)=an²+bn+1

A peaceful night for you,


I noticed for some quadratic polynomial, such as f(n)=n²+1, f(n)=2n²-1, f(n)=2n²+1 and f(n)=4n²+1 you can make a linear substitution with n=p*k+n0 with p|f(n) and p=f(n0) and a division by p so that you get
f(k)=ak²+bk+1


This seems to be something special. Do they have a mathematical name and which mathematician has investigated them ?


A short link would be really nice from you,


Greetings from Corona-times,

I live only in the night like a vampir
bhelmes is offline   Reply With Quote
Old 2021-01-24, 02:51   #2
bhelmes
 
bhelmes's Avatar
 
Mar 2016

22×89 Posts
Default

A peaceful and pleasant night,

what is the difference between eliptic curves and quadratic polynomials,
resp. what mathematical property does eliptic curves have in opposite to quadratic polynomials, especially for the factorisation.

In my opinion both are double periodically function, for both they are suitable with complex numbers and the "Ordnung" (order) is "flexible".

Would be nice if someone gives me a mathematical hint.

Greetings from the factorisation side
Bernhard

@Batalov: do you choose your avatar gif for every mail or is it random

Last fiddled with by bhelmes on 2021-01-24 at 02:53
bhelmes is offline   Reply With Quote
Old 2021-01-24, 10:14   #3
Nick
 
Nick's Avatar
 
Dec 2012
The Netherlands

17×103 Posts
Default

See "Factoring integers with elliptic curves" by H.W. Lenstra
Nick is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
primesieves for quadratic polynomials bhelmes Math 21 2020-03-19 22:14
euler phi function and quadratic irred. polynomials bhelmes Computer Science & Computational Number Theory 2 2019-08-24 15:00
the multiplicativ structur of the discriminant for quadratic polynomials bhelmes Computer Science & Computational Number Theory 3 2017-05-27 01:33
Zhang's Special Quadratic Sieve mickfrancis Factoring 2 2016-11-09 12:19
Special-q method for Quadratic Sieve mickfrancis Factoring 3 2016-05-03 08:50

All times are UTC. The time now is 03:42.


Tue Oct 26 03:42:50 UTC 2021 up 94 days, 22:11, 0 users, load averages: 1.98, 2.41, 2.24

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.