Factor Positive Integers into Primes

Related BrainMass Solutions

• Cryptography, congruences, and primes

  241057 Cryptography, congruences, and primes Hi, Can you help me with these questions? Consider the set of all even integers 2Z=....If this factorization into primes can be accomplished, is it unique?

• Proof of infinite primes

  3023 Proof of Infinite Positive Integers Prove: There are infinitely many prime numbers p of the form 4n+3. In other words, show that there exist infinitely many positive integers, n, such that the number 4n+1 is prime.

• Solving Equations

  number N, k1, k2, ... , ks are some positive integers.

• Solve Difference Equation

  number N, k1, k2, ... , ks are some positive integers.

• Determining whether or not an expression is multiplicative.

  Factor n into a product of primes,n=p1^k1* p2^k2... then set f(n)= (-1)^k1+k2+...+kr. Yes it is. We need to show f(n)f(m)=f(nm) Given two integers n and m, suppose n=p1^k1*p2^k2*...*pr^kr, m=q1^t1*q2^t2*...*qs^ts.

• Divisors and relative primes

  Thus the only value k can attain is k=1 hence and are relative primes. Alt proof: Here we use the fact that two consecutive integers are relative primes.

• Proof of the Irrationality using Euler's phi-function

  This means that for some integers p and q Square both sides Multiply both sides by q2 By Fundamental Theorem of Arithmetic, each of the integers p and q factors uniquely into primes.

• Binary Representations and Prime Factors

  (pk) +1, where p1, p2, ... pk are the kth smallest primes for all positive integers k not exceeding 50. 1. B(n) is the smallest integer which is greater than or equal to log(base 2) n.

• Discrete math proofs

  There are a series of discrete math proofs here regarding sets, relative primes, floor and ceiling, and modulo arithmetic.