Problem of the Week: 2015-03-31

Due Tuesday, March 31 at 5:00 pm

Two numbers, m and b, are chosen randomly.  The sequence {a1, a2, a3, ...} is then constructed by the rule ax = floor(mx + b), where the floor function rounds down to an integer.  The first six terms in the sequence are {4, 7, 11, 15, 18, 22, ... }.  What are the possible values of m?  Your answer will be an interval of possible values.

All answers should be clearly explained.  Mathematics is about logic and reasoning, not just about getting a number and putting a box around it.

Submit your answers to the Math/Stat Office, Room 107, Adel Mathematics Building. Please put the due date (e.g. 2015-01-13 for January 13, 2015) on your submission. Contact with questions.

Winning solutions and a summary of scores will be posted on the POTW bulletin board. This bulletin board is located near the bottom of the big stairway joining the first and second floor of the Adel Math Building.