relatively prime वाक्य
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- Three days ago I started publicly investigating a deterministic sequence of binary numbers created by prepending 1 followed by as few 0s as possible so that each succeeding number is relatively prime to all of its predecessors.
- If you are choosing large numbers sequentially so that each new one must be relatively prime to all of its predecessors, what is a good algorithm for determining each succeeding term's suitability for this?
- Just as the quadratic reciprocity law for the Legendre symbol is also true for the Jacobi symbol, the requirement that the numbers be prime is not needed; it suffices that they be odd relatively prime nonunits.
- As stated this doesn't really make sense, but is an informal way of saying that as n approaches infinity the probability that two random numbers from 1 to n are relatively prime approaches 6 / ? 2.
- Moreover, as long as the polynomial factors at each stage are relatively prime ( which for polynomials means that they have no common roots ), one can construct a dual algorithm by reversing the process with the Chinese Remainder Theorem.
- The elementary divisors can be obtained from the list of invariant factors of the module by decomposing each of them as far as possible into pairwise relatively prime ( non-unit ) factors, which will be powers of irreducible elements.
- The four linear factors p, q, p + q, and p-q are relatively prime and therefore must themselves be squares; let p + q = r ^ 2 and p-q = s ^ 2.
- It is not possible to produce a definite test of primality based on whether a number is an Euler pseudoprime because there exist " absolute Euler pseudoprimes ", numbers which are Euler pseudoprimes to every base relatively prime to themselves.
- The factors 1, 2, 4, 5, 8, 10 may start to make the pattern clear : they are those integers less than that are relatively prime to ( or have no prime factors in common with ) 21.
- The total number of positive divisors of n is a multiplicative function d ( n ), meaning that when two numbers m and n are relatively prime, then d ( mn ) = d ( m ) \ times d ( n ).
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