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).
The alogrithm here is similar to the algorithm in classical case but we choose the prime [beta] in this case from the domain of gaussian integers
For any positive integer
n [greater than or equal to] 1, the Pseudo-Smarandache function Z(n) is defined as the smallest positive integer
m such that 1 + 2 + .
It is known that they made a list of useful results on the Rhind papyrus containing the sums of reciprocal integers
for fractions of the form 2/N for all odd values of N from 5 to 101 (Wells, 1992).
Computing the variance of the 500 randomly generated integers
will require calculating and possibly storing the sum of the squares of the 500 integers
SMT solvers work by combining decision procedures for mathematical theories such as linear integer
arithmetic with a SAT solver, which assigns a true or false value to all formulas, and these combinations are much more complex and difficult to engineer than a plain SAT solver.
K(2n + 1) - K(2n) = 3n + 2, for any integer
n [member of] N.
This method of memorizing i integers
has been applied to one special numeric sequence--one's telephone number.
Although there are infinitely many primes, they are also relatively scarce and rather haphazardly scattered among the integers
m] are m positive integers
, we define the Smarandache additive sequence [D.
In 1844, Belgian mathematician Eugene Charles Catalan asserted that, among all powers of whole numbers, the only pair of consecutive integers
is 8 and 9.
That is, [phi](n) denotes the number of all positive integers
not exceeding n which are relatively prime to n.