Consider the two positive rational numbers a/b and c/d with positive
integers a, b, c and d.
Therefore the two factors on the right hand side are coprime, so we have
integers m, n such that
For example, a finite procedure that directly compares f (x) and f (y), where x and y are
integers and f is a one-to-one function, [gamma]-compares the two
integers x and y, since x = y if and only if f(x) = f(y).
Theorem 2 Let q [greater than or equal to] 3 be an odd
integer. Then for any real number N with 1 < N < [q.sup.1/6] and
integers r and s with (rs, q) = 1, we have the asymptotic formula
Discrete logarithms are perhaps simplest to understand in the group [[].sup.*.sub.p], the set of
integers {1,...., p-1} under multipication module the prime p.
In this example, samples at
integers and half points are considered.
The plain text message is encoded as blocks of sequences {[h.sub.0], [h.sub.1], [h.sub.m-1]} of
integers in [Z.sup.*.sub.N] and [h.sub.k] is encrypted as [H.sub.k] = [[beta].sup.ab] [m- 2.summation over (n=0)] [h.sub.n] [[beta].sup.nk] mod N for k = 0, 1,...,m-1.
Integer provides medical technologies to the cardiac, neuromodulation, orthopedics, vascular, advanced surgical, and portable medical markets, as well as power solutions.
Let a,b,p,k be fixed, non-zero
integers. Let 0 [not equal to] l [member of] Z.
Long
integers cover whole numbers ranging from approximately -2 billion to 2 billion.