Mathematics Problem Of the Week

Spring 2005

POW 2: Consecutive Partitions

A natural number has a consecutive partition if there exist natural numbers and such that

and

Observe that 9, 21, and 40 have the following consecutive partitions

while the numbers 2, 4, 8, and 16 have no such partition.

a). Find a consecutive partition for 100.

b). Show that every natural number has a consecutive partition if and only if

Due Friday, February 4^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/