by John Ehrke | Mar 1, 2019 | Problem of the Week
“Circular” Numbers? This problem is from Clayton Dodge. Prove that for any positive integer n, the number n2(n2-1)(n2-4) is divisible by 360. Submit your answers to mathpotw@acu.edu. Details for submissions can be found here. Solution Correct solutions...
by John Ehrke | Feb 22, 2019 | Problem of the Week
Problem 13 – February 22, 2019 Some Are Not That Far Away Consider any five points P1, P2, P3, P4, and P5 in the interior of a square of side length 1. Denote by dij the distance between points Pi and Pj when i is not equal to j. Prove that at least one of the...
by John Ehrke | Feb 8, 2019 | Problem of the Week
Problem 12 – February 8th, 2019 Is It Really One-seventh? I learned of this problem in a session on mathematics and art at the 2003 joint AMS/MAA meeting. Given any triangle ABC, construct a line from each vertex to the opposite side as indicated in the figure below....
by John Ehrke | Feb 1, 2019 | Problem of the Week
Problem 11 – February 1st, 2019 When Are There Integer Solutions? Describe all positive integers a for which the equation x2 – y2 = a has integer solutions. Submit your answers to mathpotw@acu.edu. Details for submissions can be found here. Correct...
by John Ehrke | Jan 25, 2019 | Video Spotlight
At least once per month (or more often as I run into cool stuff) I will post a video on this blog that gives insight into some cool applications of mathematics or interesting proofs and insights to mathematical techniques. The first video, linked below, is courtesy...