Abstract
One of the most fascinating rules which one learns—or used to learn—in elementary arithmetic is that of ‘casting out 9′s’. Suppose we wish to decide whether the number 758466 is divisible by 9. We may simply add the digits of the number, obtaining 36, and conclude that the number is divisible by 9 because 36 is divisible by 9. Indeed we may say more generally that if n is any number and if μ(n) is the sum of the digits of n (when n is written in the scale of 10) then n — μ(n) is always divisible by 9.
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© 1970 H. B. Griffiths and P. J. Hilton
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Griffiths, H.B., Hilton, P.J. (1970). Arithmetic Mod m . In: A Comprehensive Textbook of Classical Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6321-0_10
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DOI: https://doi.org/10.1007/978-1-4612-6321-0_10
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90342-2
Online ISBN: 978-1-4612-6321-0
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