Prove the following Let k be a natural number Then there exi

Prove the following:

Let k be a natural number. Then there exists a natural number n (which will be much larger than k) such that no natural number less than k and greater than 1 divides n.

Solution

(k-1)! is product of natural numbers from 2 to k-1 ie all natural numbres less than k and greater than k

Hence, (k-1)! is multiple of integer , m , where m is any integer from 2 to k-1

Hence, n=(k-1)!+1 is one such integer