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Unformatted text preview: Binary can be useful calculating powers mod n Math 4383 Section 4.3 Page 4 of 6 Lets revisit the divisibility test for 9 and 11 in a little more sophisticated way Theorem: If ( 29 mod a b n and P(x) is any polynomial with integer coefficients, then ( 29 ( 29 ( 29 mod P a P b . Proof: Math 4383 Section 4.3 Page 5 of 6 Consider a place value number as a polynomial with the base b the value of x So, the base ten number 35712 can be thought of as ( 29 4 3 2 3 5 7 1 2 P x x = + + + + evaluated when x = 10. Why is a number divisible by 9 when the sum of its digit is? Math 4383 Section 4.3 Page 6 of 6 What about divisibility by 11?...
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This note was uploaded on 02/21/2012 for the course MATH 4383 taught by Professor Flagg during the Spring '09 term at University of Houston.
 Spring '09
 flagg
 Number Theory, Integers

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