On Primes of the Form 2x-Q (Where Q is a Prime Less than or Equal to X) and the Product of the Distinct Prime Divisors of an Integer : A Function Approach to Proving the Goldbach Conjecture by Mathematical Induction

This paper is really an attempt to solve the age-old problem of the Goldbach Conjecture, by first restating it in terms of primes of the form 2x-q (where q is a prime less than or equal to x) and then proving the restated theorem. Restating the problem merely requires us to ask the question: Does a prime of form 2x-q lie between x and 2x? We begin by introducing the product, m, of numbers of the form 2x-q. Using the geometric series, an upper bound is estimated for the function m. A proof by contradiction is obtained when it is postulated that there are no primes of the form 2x-q. A simple multiplicative function defined as the product, (y), of the distinct prime divisors of y, is applied to m. The contradiction of a resulting inequality, using mathematical induction, then yields the required proof