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Old 2020-09-11, 16:56   #6
paulunderwood's Avatar
Sep 2002
Database er0rr

DB016 Posts

The characteristic equations of the matrices are:

x^2 - (1+u)*x + u-1 == 0 and
x^2 - (1+w)*x + w-1 == 0

The "residuals" depend on the jacobi symbol of the discriminants of these equations:

Jacobi((1+u)^2-4(u-1), n)
jacobi((1+w)^2-4(w-1), n)

If the Jacobi symbol is 1 then the matrical test is a glorified Fermat PRP test. If the symbol is -1 then it is a lucas-based test.

Recieved wisdom says that any Fermat+Lucas test has counterexamples for freely varying parameters (unless maybe the choice of u and w are more restricted -- which is what I am currently studying).

Last fiddled with by paulunderwood on 2020-09-11 at 16:57
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