### Meta

### Categories

- algebra (47)
- arithmetic (85)
- books (35)
- calculus (7)
- challenges (57)
- combinatorics (29)
- complex numbers (6)
- computation (82)
- convergence (9)
- counting (38)
- famous numbers (48)
- fibonacci (18)
- fractals (13)
- games (34)
- geometry (72)
- golden ratio (8)
- group theory (28)
- humor (8)
- induction (8)
- infinity (19)
- iteration (24)
- links (76)
- logic (9)
- meta (43)
- modular arithmetic (30)
- number theory (108)
- open problems (11)
- paradox (1)
- pascal's triangle (8)
- pattern (106)
- people (23)
- pictures (74)
- posts without words (41)
- primes (57)
- probability (9)
- programming (20)
- proof (91)
- puzzles (18)
- recursion (16)
- review (25)
- sequences (28)
- solutions (31)
- teaching (15)
- trig (3)
- Uncategorized (6)
- video (19)

### Archives

- February 2020 (1)
- January 2020 (7)
- December 2019 (4)
- November 2019 (2)
- October 2019 (5)
- September 2019 (7)
- August 2019 (3)
- July 2019 (5)
- May 2019 (4)
- April 2019 (2)
- March 2019 (3)
- February 2019 (3)
- January 2019 (4)
- November 2018 (3)
- October 2018 (4)
- September 2018 (4)
- August 2018 (6)
- July 2018 (2)
- June 2018 (5)
- May 2018 (3)
- April 2018 (5)
- March 2018 (4)
- February 2018 (3)
- January 2018 (4)
- December 2017 (3)
- November 2017 (3)
- October 2017 (1)
- September 2017 (1)
- July 2017 (4)
- June 2017 (4)
- May 2017 (9)
- April 2017 (7)
- March 2017 (5)
- February 2017 (4)
- January 2017 (3)
- December 2016 (4)
- November 2016 (6)
- October 2016 (6)
- September 2016 (2)
- August 2016 (5)
- July 2016 (2)
- June 2016 (4)
- May 2016 (4)
- April 2016 (2)
- March 2016 (3)
- February 2016 (9)
- January 2016 (8)
- December 2015 (5)
- November 2015 (29)
- August 2015 (3)
- June 2015 (2)
- April 2015 (1)
- May 2014 (1)
- December 2013 (1)
- October 2013 (1)
- July 2013 (1)
- June 2013 (1)
- May 2013 (1)
- April 2013 (3)
- March 2013 (3)
- February 2013 (2)
- January 2013 (5)
- December 2012 (3)
- November 2012 (4)
- October 2012 (5)
- September 2012 (1)
- August 2012 (4)
- July 2012 (1)
- June 2012 (6)
- May 2012 (2)
- April 2012 (3)
- March 2012 (1)
- February 2012 (4)
- January 2012 (5)
- December 2011 (1)
- November 2011 (7)
- October 2011 (4)
- September 2011 (6)
- July 2011 (2)
- June 2011 (4)
- May 2011 (5)
- April 2011 (2)
- March 2011 (4)
- February 2011 (1)
- January 2011 (1)
- December 2010 (1)
- November 2010 (4)
- October 2010 (2)
- September 2010 (1)
- August 2010 (1)
- July 2010 (1)
- June 2010 (2)
- May 2010 (3)
- April 2010 (1)
- February 2010 (6)
- January 2010 (3)
- December 2009 (8)
- November 2009 (7)
- October 2009 (3)
- September 2009 (3)
- August 2009 (1)
- June 2009 (4)
- May 2009 (5)
- April 2009 (4)
- March 2009 (2)
- February 2009 (1)
- January 2009 (7)
- December 2008 (1)
- October 2008 (2)
- September 2008 (7)
- August 2008 (1)
- July 2008 (1)
- June 2008 (1)
- April 2008 (5)
- February 2008 (4)
- January 2008 (4)
- December 2007 (3)
- November 2007 (12)
- October 2007 (2)
- September 2007 (4)
- August 2007 (3)
- July 2007 (1)
- June 2007 (3)
- May 2007 (1)
- April 2007 (4)
- March 2007 (3)
- February 2007 (7)
- January 2007 (1)
- December 2006 (2)
- October 2006 (2)
- September 2006 (6)
- July 2006 (4)
- June 2006 (2)
- May 2006 (6)
- April 2006 (3)
- March 2006 (6)

# 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

## 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