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Blast into Math! Prime nummers: indestructimle muilding mlocks

Is it possible that different natural numbers get assigned to the same integer? If n and m are different
natural numbers, then either n and m are both even, n and m are both odd, or one of them is even
and the other is odd. There are three cases, so we can prove that in each case, n and m are assigned
to different integers.

1. If n and m are both even, then because n = m , one of them is larger. By possibly
changing their names, we can assume n> m . Then it’s also true that

n m
> .
2 2

m
n
Since our algorithm assigns n to and m to , n and m are assigned to different integers.
2 2
2. If n and m are both odd, then we can again assume by possibly changing their names that
n> m . In this case n is assigned to

(n − 1)
− ,
2
and m is assigned to

(m − 1)
− .
2

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