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    Classification of Positive Integers

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    The positive integers are classified into two types, A and B; a number is A if and only if it is the sum of two (distincts) A numbers, or the sum of two (distincts) B numbers.

    a) Classify the numbers 1,2, 3 as A and B.

    b) Prove that if n, n+1, n+2 are A numbers, then every integer >= n is an A number.

    c) Find the smallest n so that every integer >= n is an A number.

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    The solution provides classification of positive integers.

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