Show that any positive even integer is of the form 6m,6m+2 or 6m+4,where m is some integer

Show that any positive even integer is of the form 6m,6m+2 or 6m+4,whe

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