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