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Tag Archives: gcd
The wizard’s rational puzzle (solutions, part 2)
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
Posted in arithmetic, challenges, logic, programming, puzzles, solutions
Tagged arithmetic, binary, denominator, Euclidean, gcd, logarithm, numerator, puzzle, rational, search, wizard
Comments Off on The wizard’s rational puzzle (solutions, part 2)
The wizard’s rational puzzle (solutions, part 1)
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 arithmetic, denominator, Euclidean, gcd, logarithm, numerator, puzzle, rational, wizard
3 Comments
From primitive roots to Euclid’s orchard
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
A few words about PWW #20
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
A few words about PWW #10
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 gcd, primitive, roots, unity
5 Comments
MaBloWriMo 24: Bezout’s identity
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 Bezout, combination, divisor, gcd, identity, linear, MaBloWriMo, proof
2 Comments