Nontrivial divisors

Related BrainMass Solutions

• Prove that a cyclic group of prime order p has no non-trivial subgroups.

  Then the subgroups of G are in bijective correspondence with the positive divisors of p, namely, 1 and p; so the only subgroups of G are G itself and the trivial subgroup - in other words, G has no nontrivial *proper* subgroups.

• Common Divisors

  58444 Common Divisors 1. Let d; a; b; r, and q be integers. a) Suppose that d|a and d|b. Show that d|(ra + qb). b) Suppose a = qb + r. Show that the set of common divisors of a and b is the set of common divisors of b and r.

• Groups : Isomorphism and Homomorphism

  15977 Groups : Isomorphism and Homomorphism Show that a group G is simple if and only if every nontrivial group homomorphism G -> G1 is one-to-one. Proof: If G is simple, then G has no nontrivial normal subgroup.

• Factoring into Prime Factors

  So, we need a method that find large prime divisors without us having to try all the previous ones. One such method is "Pollard's p-1 method" which we'll use here.

• Solving equations using the rational root theorem

  This has divisors of the form s * 2^a * 3^b * 5^c where s is a sign, and a is between 0 and 4, b is between 0 and 3 and c is between 0 and 2. This means that there are 2*5*4*3 = 120 possible divisors to check out.

• Algorithm to generate an increasing sequence of integers

  Then, there is a greatest number x (whose only prime divisors are 2 and 3) such that x = 2^i * 3^j.

• Solutions to First-Order Ordinary Differential Equations

  Thus we have whence , which yields a nontrivial solution for any constant . For instance, yields the nontrivial solution (3,3).

• Problems Involving Free Groups and Free Products

  Let g be a nontrivial element of G and h be a nontrivial element of H. Assume Z is nontrivial. Then there exists an element z of Z - {e}.

• Connected digraph proof

  This is a proof regarding Eulerian nontrivial connected digraphs.

• Graph irregularity

  98573 A nontrivial graph G is called irregular... 1.5 A nontrivial graph G is called irregular if no two vertices of G have the same degree.