Show that an even integer is of the form of 6q or 6q+ 2 or 6q+4.where q is a positive integers

Show that an even integer is of the form of 6q or 6q+ 2 or 6q+4.where

1.	Show that an even integer is of the form of 6q or 6q+ 2 or 6q+4.where q is a positive integers
Answer» Let p be any positive integerBy division algorithm, p = 6q + r, where 0 {tex} \\leqslant {/tex}r< 6Here r=0,1,2,3,4,5Therefore,values of p are : 6q, 6q + 1, 6q + 2, 6q + 3, 6q + 4, 6q + 5Now 6q+1,6q+3 and 6q+5 are odd numbers because q is a positive integer.Hence 6q, 6q + 2, 6q + 4 are even integers because they are next positive number to the odd numbers 6q-1,6q+1 and 6q+3 respectively\xa0