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Tag Archives: triangular
The route puzzle
While poking around some old files I came across this puzzle: (Click for a larger version.) I didn’t make it, and I have no idea where I got it from (do you know?). But in any case, wherever it comes … Continue reading
Posted in arithmetic, challenges, number theory, proof, puzzles
Tagged cube, perfect, prime, puzzle, route, square, triangular
7 Comments
Triangular number equations via pictures: solutions
Here are some solutions to my previous post. However, they are almost certainly not the only solutions! If you have other cool ways to visualize any of these (or any other triangular number equations) feel free to post in the … Continue reading
Posted in arithmetic, pattern, pictures, proof, solutions
Tagged number, pictures, proof without words, triangular
10 Comments
Triangular number equations via pictures
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
Triangunit divisors and quadratic reciprocity
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 OEIS, quadratic, reciprocity, triangular, triangunit
5 Comments
Triangunit divisors
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 divisors, numbers, triangular, triangunit, unit
9 Comments
Math Teachers at Play #21
Math Teachers at Play #21 is up at Math Mama Writes…, and it includes this cute puzzle, which Sue apparently made up herself: The Numberland News runs personal ads. 21 was looking for a new friend and put an ad … Continue reading
Posted in fibonacci, links, number theory, puzzles
Tagged binary, fibonacci, MTaP, palindrome, puzzle, semiprime, triangular
13 Comments