Then there exists an integer constant [C.sub.E/K] (depending on E and K) such that for all n prime to [C.sub.E/K], we have
By a theorem of Serre (, Section 4.2, Theorem 2) together with Appendix of , there exists an integer constant [C.sub.E/K] such that [rho] is surjective if n is prime to [C.sub.E/K].
Koubarakis  considers temporal difference constraint databases that contain atomic constraints of the form [x.sub.i] - [x.sub.j][Theta]c, where [x.sub.i], [x.sub.j] are integer variables, c is an integer constant, and [Theta] is one of = , [is greater than or equal to].
Having an empty edge relation assures that in the relation to be negated there is no constraint of the form x [[is less than].sub.g] y where x, y are variables and g is any nonnegative integer constant.
It is easy to see that Theorem 6.5 is true even if the size of each integer constant occuring in the input database d is logarithmic in the size of d.
Let c, d, p, m, t, l, b be the integer constants denoting the id numbers of the candidate team members.
If we do not restrict the size of the integer constants in the input database, then d may contain the relation two_to_s([2.sup.s], as well as no_digits(s) and the next relation from next(0,1) to next(s - 1, s).
Assuming that m, a, q and r are global integer constants
and that s is a global integer variable holding the current variate, (14) can be implemented as follows (using Pascal-like syntax): k := s DIV q; s := a * (s - k * Q) - k * r; IF s < 0 THEN s := s + m