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hpr1292 :: Doomsday Remainders

Reflections on remainders inspired by Doomsday Rule sign-off. Applications to programming and arithm

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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

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

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