Question

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

Answer 1

Dear student,
Let ‘a’ be any positive even integer and ‘b = 6’.
Therefore, a = 6m +r, where 0 ≤ r < 6.
Case 1 r = 0, we get, a = 6m + 0 = 6m , Even(6) x m = Even
Case 2 r = 1, we get, a = 6m +1, Odd
Case 3 r = 2, we get, a = 6m + 2, Even
Case 3 r = 3, we get, a = 6m + 3, Odd
Case 4 r = 4, we get, a = 6m + 4, Even
Case 5 r = 5, we get, a = 6m +5, Odd
Therefore, 6m or, 6m + 2 or, 6m + 4 are the forms of any positive even integers.

Regards