Pages

Thursday, April 10, 2008

Problem ( Number Theory )

Let m, n be positive integers.

Show that:

If 24 / ( m * n + 1 ) Then 24 / ( m + n ).

1 comment:

  1. Say (mn + 1)| 24 (| denotes divisibility of 24 by mn + 1). Now, since 24 = 2.2.2.3, we must have:

    (mn + 1)| 2 or (mn + 1)| 3.

    In the former case: mn + 1 = 2, since 2 is prime and mn + 1 > 1. So mn = 1.

    In the latter case, similarly, mn + 1 = 3, so mn = 2.

    In either case, mn | 24.

    ReplyDelete