Number Theory Warmups

Obviously, not all numbers are created equal, but number do share some fascinating properties. Examine the set of natural numbers in a way you've never seen before and find some truly beautiful and deep connections between them.

For example, have you ever wondered why 1, 5, and 6 are the only numbers which, when squared, have units digits equal to the original number? And why isn't 1 considered a prime number?

If you’re just beginning to use Brilliant as a way to improve your mathematical prowess, here’s the essence of Brilliant’s approach: solve problems. Here are some quick tips for strengthening your number theory problem-solving skills:

• When you first approach a new question, ask yourself: "what are the properties of the numbers and operations involved in this question?"
• The only even prime number is 2, and the number 1 is not a prime!
• Understanding why rules and theorems work makes it easy for you to remember them.