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Strong Frobenius Pseudoprime


A pseudoprime which obeys an additional restriction beyond that required for a Frobenius pseudoprime. A number n with (n,2a)=1 is a strong Frobenius pseudoprime with respect to x-a iff n is a strong pseudoprime with respect to f(x). Every strong Frobenius pseudoprime with respect to x-a is an Euler pseudoprime to the base a.

Every strong Frobenius pseudoprime with respect to f(x)=x^2-bx-c such that ((b^2+4c)/n)=-1 is a strong Lucas pseudoprime with parameters (b,c). Every strong Frobenius pseudoprime n with respect to x^2-bx+1 is an extra strong Lucas pseudoprime to the base b.


See also

Frobenius Pseudoprime

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References

Grantham, J. "Frobenius Pseudoprimes." 1996. http://www.clark.net/pub/grantham/pseudo/pseudo1.ps.

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Strong Frobenius Pseudoprime

Cite this as:

Weisstein, Eric W. "Strong Frobenius Pseudoprime." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/StrongFrobeniusPseudoprime.html

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