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Let A and B be any sets, and let |X| be the cardinal number of a set X. Then cardinal exponentiation is defined by |A|^(|B|)=|set of all functions from B into A| (Ciesielski ...

Let A and B be any sets. Then the product of |A| and |B| is defined as the Cartesian product |A|*|B|=|A×B| (Ciesielski 1997, p. 68; Dauben 1990, p. 173; Moore 1982, p. 37; ...

Given a set P of primes, a field K is called a class field if it is a maximal normal extension of the rationals which splits all of the primes in P, and if P is the maximal ...

The term "continuum" has (at least) two distinct technical meanings in mathematics. The first is a compact connected metric space (Kuratowski 1968; Lewis 1983, pp. 361-394; ...

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.

There are so many theorems due to Fermat that the term "Fermat's theorem" is best avoided unless augmented by a description of which theorem of Fermat is under discussion. ...

A fractional ideal is a generalization of an ideal in a ring R. Instead, a fractional ideal is contained in the number field F, but has the property that there is an element ...

A group homomorphism is a map f:G->H between two groups such that the group operation is preserved:f(g_1g_2)=f(g_1)f(g_2) for all g_1,g_2 in G, where the product on the ...

The ordered pair (s,t), where s is the number of real embeddings of the number field and t is the number of complex-conjugate pairs of embeddings. The degree of the number ...

Every sufficiently large odd number is a sum of three primes (Vinogradov 1937). Ramachandra and Sankaranarayanan (1997) have shown that for sufficiently large n, the error ...