Monthly Archives: March 2011

Triangular number equations via pictures

Posted on March 24, 2011 by Brent

The other day I was fiddling around a bit with triangular numbers. By only drawing pictures I was able to come up with the following triangular number equations, where denotes the th triangular number (that is, the number of dots … Continue reading →

Posted in challenges, pictures, proof | Tagged , , , | 8 Comments

Triangunit divisors and quadratic reciprocity

Posted on March 20, 2011 by Brent

Recall that the triangunit numbers are defined as the numbers you get by appending the digit 1 to the end of triangular numbers. Put another way, where denotes the th triangular number, and the th triangunit number. The challenge, posed … Continue reading →

Posted in arithmetic, modular arithmetic, number theory, primes, proof | Tagged , , , , | 5 Comments

Moved to wordpress.com

Posted on March 20, 2011 by Brent

I spoke too soon before — over the past several weeks I’ve continued to have problems with my hosting, so I finally bit the bullet and transferred everything to wordpress.com (the URL of my blog is the same as before … Continue reading →

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Triangunit divisors

Posted on March 1, 2011 by Brent

Here’s a neat problem from Patrick Vennebush of Math Jokes 4 Mathy Folks: Append the digit 1 to the end of every triangular number. For instance, from 3 you’d get 31, and from 666 you’d get 6,661. Now take a … Continue reading →

Posted in number theory, pattern, puzzles | Tagged , , , , | 9 Comments