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.
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
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