Problems

The following problems are printed in the January 1997 issue. Solutions will be printed in future issues.
Solutions for theses problems should be mailed before April 30, 1997. (Solutions sent after that date will be considered as deadlines permit.)

With the January issue we began a new feature of the SSM Problem Department - an Oldie But Goodie problem. We have selected some of our favorite problems that have appeared in this department since it began in 1905 and will feature one in each issue.

4548S: Student Problem - only undergraduate and pre-college students are eligible to submit a solution.
Proposed by Murray S. Klamkin, Edmonton, Alberta, Canada.
Prove that the points of intersection of two parabolas whose axes are orthogonal lie on a circle.
Editors' Note: This problem appeared originally in the January, 1996 issue. Since no solutions were received, the problem remains "open" until April 30, 1997.

45960BG: Oldie But Goodie - Proposed by Ira M. Delong, Boulder, CO.
A man and a boy agree to dig a patch of potatoes for ten dollars. The man can dig as fast as the boy can pull tops, and he can pull tops twice as fast as the boy can dig. How should the money be divided?

4597: Proposed by V.C. Bailey, Naples, FL.

4598: Proposed by Michael Brozinsky, West Hempstead, NY.

4599: Proposed by Russell Euler, Maryville, MO.

4600: Proposed by Richard L. Francis, Cape Girardeau, MO.
Let T_l, T₂ be transcendental numbers. Show that at least one of the two numbers T₁ + T₂, T_lT₂ must be transcendental.

4601: Proposed by J. Sriskandarajah. Richland Center, WI.
Determine a "non-trivial" function f(x, y, z) which produces a square nurhber if x, y, z are consecutive square numbers.