Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.
This is a beautiful result involving a parabola and parallels.
Given any 3 digit number you can use the given digits and name another number which is divisible by 37 (e.g. given 628 you say 628371 is divisible by 37 because you know that 6+3 = 2+7 = 8+1 = 9). The question asks you to explain the trick.
If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.
A composite number is one that is neither prime nor 1. Show that 10201 is composite in any base.
Weekly Problem 26 - 2008
If $n$ is a positive integer, how many different values for the remainder are obtained when $n^2$ is divided by $n+4$?
Explore what happens when you draw graphs of quadratic equations with coefficients based on a geometric sequence.
