positive integer


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positive integer

[¦päz·əd·iv ′int·i·jər]
(mathematics)
An integer greater than zero; one of the numbers 1,2,3,….
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Since deg(g) = deg(f) [greater than or equal to] 2, we see that 0 < [([D.sub.n]).sup.k] < 1 for a sufficiently positive integer n.
Algorithm 2 Let n be a nonnegative integer, [lambda] [member of] C, and k be a positive integer. This algorithm will return the numbers Wn ([lambda]) recursively with the help of the procedure W_APOSTOL_TYPE_NUM given by Algorithm 1.
Let p be a prime and e [greater than or equal to] 2, k [greater than or equal to] 2 be two positive integers. Let h be the unique positive integer such that [k.sup.h-1] < e [less than or equal to] [k.sup.h].
Let N be a positive integer. Then N is a trapezoidal number if and only if N is not of the form [2.sup.i] for all i [member of] N [union] {0}.
From (37) and (46) we see that [[??].sub.k](n) = [S.sub.k](n) for each n = 1, 2, ..., and thus the polynomial identity (45) with respect to the positive integer variable n can be extended to the real variable x instead of n; that is, (45) is identically satisfied (on R) if we replace [S.sub.l](n) by [[??].sub.i](x) (with l = 2k + 1 and l = 2i).
where p, q are any two positive integers with p [greater than or equal to] q.
If, for some positive integer k and [alpha] [greater than or equal to] 0, ([[tau].sub.n]) is [(A).sup.(k)](C, [alpha]) summable to s and
Since M is [pi]-Rickart, [r.sub.M] ([f.sup.n]) = eM for some positive integer n and [e.sup.2] = e [member of] S.
where q is any positive integer such that m [greater than or equal to] q.
We recall that the LCM of two whole numbers a and b is the smallest positive integer having both a and b as factors (see Burton, 2002, p.
The Beal Conjecture states that the only solutions to the equation Ax + By = Cz, when A, B, C, are positive integers, and x, y, and z are positive integers greater than two, are those in which A, B, and C have a common factor.
Inspired by the above conclusions, in this paper, we study the hybrid mean value properties of the Smarandache kn-digital sequence with SL(n) function and divisor function d(n), where SL(n) is defined as the smallest positive integer k such that n|[1, 2,...,k], that is SL(n) = min{k : k [member of] N, n|[1, 2,..., k]}.

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