Problems

Volume 96(6), October 1996

Volume 96(6)

The following problems are printed in the October 1996 issue. Solutions will be printed in future issues.
Solutions for theses problems should be mailed before January 31, 1997. (Solutions received after that date will be considered as deadlines permit.)

4531: Proposed by Edward Early and Alexander Saltrnan, students at the Science Academy of Austin at LBJ, Austin, TX.

Editors' Note: This problem appeared originally in the October, 1995 issue. Since no solutions were received, the problem remains "open" until January 31, 1997.

4578S: Student Problem - only undergraduate and pre-college students are eligible to submit a solution.
Proposed by Herta T. Freitag, Roanoke, VA.

4579: Proposed by Titu Andreescu, Aurora, IL.

4580: Proposed by V. C. Bailey, Naples, FL.

4581: Proposed by Richard L. Francis, Cape Girardeau, MO.
A set of positive integers is rigid if no permutation of the digits of any of its elements forms a different element of the set.
(a) Show that the set of squares, the set of cubes, and the set of primes are not not rigid.
(b) Show that the set of even perfect numbers is rigid.

4582: Proposed by John P. Hoyt, Lancaster, PA.

4583: Proposed by Charles Ashbacher, Cedar Rapids, IA.