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Old 2021-01-05, 01:42   #1
bhelmes
 
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Mar 2016

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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,


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