Tag Archives: gcd

The wizard’s rational puzzle (solutions, part 2)

Posted on November 9, 2018 by Brent

At long last, here is the solution I had in mind for the Wizard’s rational puzzle. Recall that the goal is to figure out the numerator and denominator of a secret rational number, if all we are allowed to do … Continue reading →

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The wizard’s rational puzzle (solutions, part 1)

Posted on October 24, 2018 by Brent

About two and a half months ago I posted a challenge involving a sadistic math wizard, metal cubes containing rational numbers, and a room full of strange machines. I’ve been remiss in following up with some solutions. (Go read the … Continue reading →

Posted in arithmetic, challenges, logic, programming, puzzles, solutions | Tagged , , , , , , , , | 3 Comments

From primitive roots to Euclid’s orchard

Posted on July 26, 2017 by Brent

Commenter Snowball pointed out the similarity between Euclid’s Orchard… …and this picture of primitive roots I made a year ago: At first I didn’t see the connection, but Snowball was absolutely right. Once I understood it, I made this little … Continue reading →

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A few words about PWW #20

Posted on July 22, 2017 by Brent

A couple commenters quickly figured out what my previous post without words was about. The dots making up the image are at integer grid points , with the center at . There is a dot at if and only if … Continue reading →

Posted in pattern, pictures, posts without words | Tagged , , | 10 Comments

Post without words #20

Posted on July 8, 2017 by Brent
Posted in pattern, pictures, posts without words | Tagged , , | 7 Comments

A few words about PWW #10

Posted on August 30, 2016 by Brent

If you still want to think more about the picture in my previous post, stop reading now! Here’s a simple way to think about how the picture is made, as noted by Fergal Daly. The th circle (starting with ) … Continue reading →

Posted in geometry, pattern, pictures, posts without words | Tagged , , , | 5 Comments

MaBloWriMo 24: Bezout’s identity

Posted on November 25, 2015 by Brent

A few days ago we made use of Bézout’s Identity, which states that if and have a greatest common divisor , then there exist integers and such that . For completeness, let’s prove it. Consider the set of all linear … Continue reading →

Posted in algebra, arithmetic, modular arithmetic, number theory | Tagged , , , , , , , | 2 Comments