In the Fun Fact Sums of Two Squares, we’ve seen which numbers can be written as the sum of two squares....
Continue reading...number theory
Quick Square Roots
Here’s a very quick way to generate the square root of N. Let A0=N. Then generate a sequence of numbers A1, A2,...
Continue reading...Repunit Fun
A repunit is a whole number consisting of only 1’s, such as 1, 111, or 111111111. (It’s like a repeating unit.) These numbers have...
Continue reading...Divisibility by Eleven
It is easy to tell that the following are multiples of 11: 22, 33, 44, 55, etc. But how about:...
Continue reading...Why Does 0.999… = 1?
Consider the real number that is represented by a zero and a decimal point, followed by a never-ending string of...
Continue reading...tamreF’s Last Theorem
Here’s an amusing theorem that is very easy to prove, which we’ll call tamreF’s Last Theorem. In fact it is tamreF’s...
Continue reading...Gaps in Primes
We know there are infinitely many primes, so are many interesting questions you can ask about the distribution of primes, i.e., how...
Continue reading...Repeating Digits
You already know that the decimal expansion of a rational number eventually repeats or terminates (which can be viewed as a repeating...
Continue reading...Hailstone Numbers
Start with any positive integer (an initial seed) and obtain a sequence of numbers by following these rules. 1. If the...
Continue reading...Fermat’s Little Theorem
Fermat’s little theorem gives a condition that a prime must satisfy: Theorem. If P is a prime, then for any...
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