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The procedure used in subtraction to "borrow" 10 from the next higher digit column in order to obtain a positive difference in the column in question.

Solve the Pell equation x^2-92y^2=1 in integers. The smallest solution is x=1151, y=120.

The value of b, where a=b (mod m), taken to be nonnegative and smaller than m.

A group of sociable numbers of order 3.

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.

Two quantities y and x are said to be directly proportional, proportional, or "in direct proportion" if y is given by a constant multiple of x, i.e., y=cx for c a constant. ...

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 ...