Question

Prove that if any positive integer is of the form 6q+5,
then it is of the form 3q+2 for some integer q , but not conversely.

explain your answer !!!

Answer 1

let us consider any number of the form N = 6q+5=3*2q+3+2=3*(2q+1)+2 where 'q' is equal to 2q+1 which will be positive integer since q is also integer. where as if the number is of the form N=3q+2=3*(q+1)+2=3q+5=6*q/2+5
here since q is an integer then q-1 = q is also an integer but it doesn't gaurantee that q/2 is also an integer there the converse is not definitely true