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A sequence {a_1,a_2,...} for which a_1>=a_2>=....

The difference of two numbers n_1 and n_2 is n_1-n_2, where the minus sign denotes subtraction.

A field K is said to be an extension field (or field extension, or extension), denoted K/F, of a field F if F is a subfield of K. For example, the complex numbers are an ...

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

The double-struck capital letter I, I, is a symbol sometimes used instead of Z for the ring of integers. In contrast, the lower case symbol i is used to refer to the ...

An operator A^~ such that A^~^2=A^~ or an element of an algebra x such that x^2=x.

A divisor which is not a proper divisor.

For a sequence {a_n}, if a_(n+1)-a_n>0 for n>=x, then a_n is increasing for n>=x. Conversely, if a_(n+1)-a_n<0 for n>=x, then a_n is decreasing for n>=x. If a_n>0 and ...

A quantity from which another (the subtrahend) is subtracted.

If the first case of Fermat's last theorem is false for the prime exponent p, then 3^(p-1)=1 (mod p^2).