Analyze (6, 9, 20)-accessibility. 1. We have broken the positive integers into t

Question

Analyze (6, 9, 20)-accessibility.

1. We have broken the positive integers into two families, based on remainders when divided by 2, and three families, based on remainders when divided by 3. Observe that the positive integers can also be broken into six families, depending on what their remainders are when divided by 6.

2. Write down the first few positive integers in each of the six families. For instance, one family begins with 1, 7, 13, 19, 25, 31, 37, 43, 49.

3. For each of the six lists, find the first number in the list that is (6, 9, 20)- accessible.

4. Explain why every number after that number in the list is also (6, 9, 20)- accessible.

Explanation / Answer

2.

The first few positive integers of the 6 families are as under:

        i.     1,7,13,19,25,31,37,43,49,55,61,….

      ii.    2,8,14,20,26,32,38,44,51,58,64,…

        iii.   3,9,15,21,27,33,39,45,51,57,63,69,….

        iv.   4, 10,16,22,28,34,40,46,52,58,64,70,…

        v.    5, 11,17,23,29,35,51,57,63,69,75,82,…

        vi.    6,12,18,24,30,36,42,48,54,60,66,72,78,…

3.

The 1st numbers in the lists that is 6,9,20- accessible are as under:

        i.     49( 9,20,20)

        ii.   20 (20)

        iii.   9(9)

        iv.   40(20,20)

       v.    29(9,20)

       vi.   6(6)

    vi.    6,12,18,24,30,36,42,48,54,60,66,72,78,…

4. Every succeeding number in each family after first number in the list that is (6, 9, 20)- accessible is 6 + this number. Hence every such number is (6,9,20) – accessible.

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