WEEK ONE: Divisor Diversions
Solutions due by high noon on Friday, Sept 5.
Define a function g(n) as follows. For any positive integer n greater than 1, determine the largest divisor of n other than n itself. We let g(n) equal one more than this divisor. For instance, g(39)=14, since the largest divisor of 39 (other than 39 itself) is 13, and adding 1 gives 14.
(a) Find all positive integers n for which g(n)=50.
(b) For how many integers n from 2 to 100 do we have g(g(n))=2?
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This problem is brought to you by Sam Vandervelde.
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