by John Ehrke | Sep 17, 2020 | Problem of the Week
Symmetric Functions I This problem is from Alexander Karabegov. Given a quadratic polynomial x2 + p x + q with two real roots s and t, express the following functions of s and t as polynomials in p and q. s + t st s2 + t2 s3 + t3 Please submit all problem solutions to...
by John Ehrke | Feb 28, 2020 | Problem of the Week
An Easy Fermat Case Find all solutions in integers of x2 + y2 = z2, with x, y, and z in arithmetic progression. Please submit all problem solutions to mathpotw@acu.edu before 5:00 PM on March 5th.
by John Ehrke | Feb 21, 2020 | Problem of the Week
Where Does It Happen? This problem is from Jason Holland. Let x1, x2, x3, x4 be real numbers such that x2 – x1 = x3 – x2 = x4 – x3 = 1. Prove that the product x1x2x3x4 is never less than -1, but can equal -1. Find all lists (x1, x2, x3, x4) for which...
by John Ehrke | Feb 7, 2020 | Problem of the Week
Discover Something Let N be one more than the product of four consecutive positive integers. What can you say about N? Prove it. (Of course, what you say about N must have some substance. Trivial statements are unacceptable.) Please submit your work to...
by John Ehrke | Jan 27, 2020 | Problem of the Week
Win the Contest This problem is from Grant Fikes. Every year at the annual Winter Wizard World conference, there is a contest for student teams from each of the wizard training schools. This year each team has five student members, and each member of each team has...
