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Old 2021-09-09, 23:05   #1
bhelmes
 
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Mar 2016

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Default speed up by a linear substitution of a quadratic polynomial ?

A peaceful and pleasant day for you,

Let f(n)=2n²-1 and the linear substitution n=Mp*k+1, Mp is the exponent of the coresponding Mersenne number

I know that there is a factor g | f(n0) if 2^Mp-1 is not prime.
I think the quadratic polynomial after the linear substitution contains also the same g | f(k0)

Is it right that the linear substitution speed up the search for g by successiv increasing the k with one ?

P.S. @Dr Sardonicus, I appreciate your answers, clear words with logical constructions, thanks for that.
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