HPR1292: Doomsday Remainders

Last Episode on Conway's Doomsday Rule ends with teaser on MOD(), a
"remainder" function defined for integer values (whole numbers):

   MOD(K, m) = remainder when K is divided by "modulus" m.
   
Examples: 
  a. MOD(207, 7) = MOD(207 - 140, 7) = MOD(67, 7) = 4
  b. MOD(1234567, 2) = 1 because the number is odd
  
MOD() function found in most spreadsheet programs, but it also shows up
as an operator in some programming languages: (a % b), or (a mod b).


Other functions referenced:
   DIV(K, m)    = quotient in integer division
      where K = m * quotient + remainder (not returned)
            0 <= remainder < m

   DIVMOD(K, m) = (quotient, remainder) when K is divided by m
      where remainder = MOD(K, m)
            quotient  = DIV(K, m)
            K = m * quotient + remainder

Full Show Notes

https://hackerpublicradio.org/eps/hpr1292.txt

Links

• https://en.wikipedia.org/wiki/Modular_arithmetic
• https://www.khanacademy.org/math/applied-math/cryptography/modarithmetic/a/what-is-modular-arithmetic
• https://betterexplained.com/articles/fun-with-modular-arithmetic/
• https://mathworld.wolfram.com/Congruence.html
• https://en.wikipedia.org/wiki/ALGOL_60
• https://www.conservapedia.com/Pascal_%28programming_language%29
• https://www.gnu.org/software/libc/manual/html_node/Integer-Division.html#Integer-Division
• https://www.haskell.org/tutorial/numbers.html
• https://www.standardml.org/Basis/integer.html
• https://docs.python.org/2/library/functions.html#divmod
• https://docs.python.org/3/library/functions.html#divmod
• https://ruby-doc.org/core-2.0/Numeric.html
• https://en.wikipedia.org/wiki/Doomsday_rule
• https://en.wikipedia.org/wiki/Modulus_operation
• https://zetcode.com/lang/python/lists/
• https://docs.python.org/2/tutorial/introduction.html

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