mersenneforum.org - View Single Post - special quadratic polynomials : f(n)=an²+bn+1

bhelmes · 2021-01-05, 01:42

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

2021-01-05, 01:42	#1
bhelmes Mar 2016 2·7·23 Posts	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