1 Let n be a

positive integer and a, b, c and q parameters.

N] secret key of A and k is the largest

positive integer less than [phi](N) relatively prime with [phi](N).

MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for all

positive integers q and each fixed m, n = 1,2,3, .

They therefore needed a simple test to determine whether a given form represents all

positive integers.

By replacing the number 3 with the

positive integer n, the last example may be generalized to give a function that answers the question posed above.

Let N represent any

positive integer, then (N + 1) is the next one, and so N and (N + 1) are consecutive.

alpha]] as the generating function of column-strict composition tableaux, which are certain fillings of strong composition shape [alpha] with

positive integers.

In 1770, French mathematician Joseph-Louis Lagrange proved what Diophantus, Pierre de Fermat, and others previously assumed: Every

positive integer is either a square itself or the sum of two, three, or four squares.

Sums of powers and sums of products of

positive integers occur in many combinatorial problems.

We just prove the case of k = 3 and k = 5, for other

positive integers we can use the similar methods.

Difficulties occur in moving from such intuitive understandings to formal mathematical representations of operations with negative and

positive integers.

We index the cells of a diagram by (row, column) pairs of

positive integers.