Mathematics Problem Of the Week

Spring 2008

POW #9

Sixes and Sevens

An interesting and little known fact is that 7 divides 767,557 and 7 also divides 767 – 557 = 210.

Show that 7 divides a six-digit number if and only if it divides the difference of the first three digits and the second three digits read as three-digit numbers. That is, 7 divides abcdef if and only if 7 divides abc – def.

Due Friday, April 4^th at Noon.

Solutions should be submitted to Dr. R. Lock's mailbox in the Math/CS/Stat office or sent via e-mail to rlock@stlawu.edu.