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Let be the proposition that can be represented as the sum of nonnegative integer multiples of 6, 7 and 17.
We assume that is nonempty.
Then by the Well Ordering Principle, there is a smallest number, .
Since , it follows that and is true.
But if is true, then must be true. Contradiction.
(if can be represented as the sum of nonnegative integer multiples of 6, 7 and 17, then we can add 6 and get representation for number )
So, is empty and is true for .