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For p an odd prime and a positive integer a which is not a multiple of p, a^((p-1)/2)=(a/p) (mod p), where (a|p) is the Legendre symbol.

Let p_i denote the ith prime, and write m=product_(i)p_i^(v_i). Then the exponent vector is v(m)=(v_1,v_2,...).

A mathematical object invented to solve irreducible congruences of the form F(x)=0 (mod p), where p is prime.

The Fermat number F_n is prime iff 3^(2^(2^n-1))=-1 (mod F_n).

A nonzero and noninvertible element a of a ring R which generates a prime ideal. It can also be characterized by the condition that whenever a divides a product in R, a ...

1 and -1 are the only integers which divide every integer. They are therefore called the prime units.

There exist infinitely many n>0 with p_n^2>p_(n-i)p_(n+i) for all i<n, where p_n is the nth prime. Also, there exist infinitely many n>0 such that 2p_n<p_(n-i)+p_(n+i) for ...

An algorithm which finds the least nonnegative value of sqrt(a (mod p)) for given a and prime p.

A homogeneous ideal defining a projective algebraic variety is unmixed if it has no embedded prime divisors.

Let N be an odd integer, and assume there exists a Lucas sequence {U_n} with associated Sylvester cyclotomic numbers {Q_n} such that there is an n>sqrt(N) (with n and N ...