# High School Challenge

# Conversely Speaking

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Start with a theorem and then take its converse to make a new hypothesis.
Sometimes this converse is true and sometimes it is not. For example: If A
is a factor of B, then A^A is a factor of B^B (A and B are whole numbers).
If A^A is a factor of B^B, must A be a factor of B?

Either prove that A must be a factor of B, when A^A is a factor of B^B, or
give a counter-example.

####
Professor Tom Butts, University of Texas at Dallas gave this problem at a
school awards function and it was submitted by Beth Wilson, Apollo JHS,
Richardson, TX.

### Correct Solutions:

- Xingji Zheng. Abby Senior SS, Abbotsford, BC, Canada
- Sorin Ionescu. Ecole Secondaire Dorval, Dorval, Quebec, Canada
- Tanvir Prince. Chrishtopher Columbus HS, Bronx NY
- Lars Erik Walle. Thor Heyerdahl VGS, Larvik, Norway
- Ken Scheiwe. New Trier HS, Wilmette, IL
- Yang Liu. Davis HS, Davis, CA
- Paul Pollack. Gulf HS, New Port Richey, FL
- Ranen Ghosh. Spruce Creek HS, Port Orange, FL
- Justin Lam. College Park HS, Pleasant Hill, CA
- Jesse Carlin. Salmen HS, Slidell, LA
- Randal West. Spruce Creek HS, Port Orange, FL
- Ido Yariv. Gan-Nachum School, Rishon LeZion, Israel
- Torbjoern Elvsaashagen. Thor Heyerdahl VGS, Larvik, Norway