Problems

The following problems are printed in the November 1997 issue. Solutions will be printed in future issues.
Solutions for theses problems should be mailed before January 31, 1998. (Solutions sent after that date will be considered as deadlines permit.)

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

Editors' Note: This problem appeared originally in the May, 1996 issue. Since no solutions were received, the problem remains "open" until January 31, 1998.

4626-OBG: Oldie But Goodie
Proposed by Norman Anning, Chilliwick, BC, Canada
A, B, and C are any three points in a plane. With center B a circle-quadrant CQ, with center A a quadrant QR, with center B a quadrant RS, and with center A a quadrant ST are described, all in the same direction of turning. Prove that T and C coincide.

4627: Proposed by V. C. Bailey, Naples, FL.

4628: Proposed by Richard L. Francis, Cape Girardeau, MO.
In noting that the perfect number 28 can be expressed as the sum of two cubes, namely l³ + 2³ = 28, the counterpart question for squares arises. Can an even perfect number be expressed as the sum of two squares?

4629: Proposed by Ghunaym M. Ghunaym, Albany, GA.
(a) Prove that the equation

where a, b, c, d, e, f, g are integers, has an infinite number of solutions.
(b) If e = 1995, f = 1996 and g = 1997, find a, b, c and d.

4630: Proposed by Kenichiro Kashihara, Sagamihara, Japan

4631: Proposed by Heinz-Jürgcn Seiffert, Berlin, Germany.

(For a related problem, see Problem 10494 and its solution in the April 1997 issue of the American Mathematical Monthly.)