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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. ...

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.

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 ...