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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.

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(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)