Question

Joseph Louis Lagrange​ (1736-1813) conjectured that every odd natural number greater than 5 can be written as a sum a plus 2 b​, where a and b are both primes. ​(a) Verify this for the odd natural number 11. ​(b) Verify that the odd natural number 17 can be written in this form in four different ways.

Answer 1

Explanation:

(a) 11 can be written as (5+2*3), being 5 and 3 prime numbers

(b) 17 can be written as:

3 + 2*7 = 17

7 * 2*5 = 17

11 + 2*3 = 17

13 + 2*2 = 17

CHECK!!