number theory, the Fermatpseudoprimes make up the most important class of pseudoprimes that come from Fermat's little theorem. Fermat's little theorem states...
composites also pass, making them "pseudoprimes". Unlike the Fermatpseudoprimes, for which there exist numbers that are pseudoprimes to all coprime bases (the...
a Dickson pseudoprime with parameters ( P , Q ) {\displaystyle (P,Q)} , since it is defined by conditions (1) and (3'); a Fermatpseudoprime base | Q |...
Carmichael numbers are also called Fermatpseudoprimes or absolute Fermatpseudoprimes. A Carmichael number will pass a Fermat primality test to every base...
are twice as strong as tests based on Fermat's little theorem. Every Euler pseudoprime is also a Fermatpseudoprime. It is not possible to produce a definite...
composite Fermat number is a strong pseudoprime to base 2. This is because all strong pseudoprimes to base 2 are also Fermatpseudoprimes – i.e., 2 F...
Lucas pseudoprimes and Fibonacci pseudoprimes are composite integers that pass certain tests which all primes and very few composite numbers pass: in...
Fermat number Fermat point Fermat–Weber problem Fermat polygonal number theorem Fermat polynomial Fermat primality test FermatpseudoprimeFermat quintic threefold...
1{\pmod {n}}} when n is composite is known as a Fermat liar. In this case n is called Fermatpseudoprime to base a. If we do pick an a such that a n − 1...
de Fermat stated (without proof) Fermat's little theorem (later proved by Leibniz and Euler). Fermat also investigated the primality of the Fermat numbers...
If n is composite and satisfies the formula, then n is a Fibonacci pseudoprime. When m is large – say a 500-bit number – then we can calculate Fm (mod...
only probabilistic, the probability of the Fermat test finding a Fermatpseudoprime that is not prime is vastly lower than the error rate of the Lucas-Lehmer...
three nonzero triangular numbers must exist. This is a special case of the Fermat polygonal number theorem. The largest triangular number of the form 2k − 1...
number (like 257) that is one more than a positive power of two is called a Fermat prime—the exponent itself is a power of two. A fraction that has a power...
All composite divisors of prime-exponent Mersenne numbers are strong pseudoprimes to the base 2. With the exception of 1, a Mersenne number cannot be a...
In number theory, a pseudoprime is called an elliptic pseudoprime for (E, P), where E is an elliptic curve defined over the field of rational numbers...
The modern study of figurate numbers goes back to Pierre de Fermat, specifically the Fermat polygonal number theorem. Later, it became a significant topic...
( 2 n + 1 ) {\displaystyle 2^{n-1}(2^{n}+1)} formed as the product of a Fermat prime 2 n + 1 {\displaystyle 2^{n}+1} with a power of two in a similar way...
identity – Product of sums of four squares expressed as a sum of four squares Fermat's theorem on sums of two squares – Condition under which an odd prime is...
problem). Fermat knew that a fourth power cannot be the sum of two other fourth powers (the n = 4 case of Fermat's Last Theorem; see Fermat's right triangle...
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