Problem of the Week

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.

Submit your solutions to Choong-Soo Lee.  You may submit either a hard copy or an electronic file.  Good luck!

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