Forum de mathématiques - Bibm@th.net

oussama

Membre

Inscription : 23-09-2014

Messages : 1

theory of numbers

use Bertrand`s postulate to show that every positive integer n ≥7 is the sum of distinct primes .( with reduction please )

Fred

Administrateur

Inscription : 26-09-2005

Messages : 7 352

Re : theory of numbers

That's strange. Why so many questions in english???

Even if you do not speak french very well, be careful. In this forum, we have to say "Hello!".

Coming back to your problem, you can do it by induction on n. This works for n=7,8,9,10,...,15 (easy to check).
Suppose that it holds until n>14. Then, by Bertrand's postulate, there is a prime number
p in [(n-7)/2, n-7].
Then n-p is larger than, or equal to 7. And n-p is less than n-1. So you can apply the induction hypothesis to n-p.

Fred.