Mathematics Problem Of the Week

Spring 2007

POW 3: Reciprocal Integrity

Consider all real numbers x such that

is an integer.

(a) Find at least 7 real numbers that give an integer when added to their reciprocal.

(b) Find all rational numbers that have this property.

Justify your answers in each case.

Due Friday, February 9^th, at Noon.

Solutions should be submitted to Dr. Maegan Bos’ mailbox in the Math office or sent via e-mail to mbos@stlawu.edu

Presentation counts! The prize-winning entry will be selected from all correct submissions, based on the clarity, creativity and elegance of the solution.

Look for the SLU POW on the Web at http://it.stlawu.edu/~math/activities/