Unformatted text preview: (b) Determine the value of the digit a such that the number 2178a22503 is a valid ISBN. (c) When an ISBN was copied, two adjacent digits were interchanged resulting in the number 1183976045. Determine the original ISBN. Problem 2 . A positive integer is divisible by 8 if and only if the threedigit integer formed by its ﬁnal three digits is divisible by 8. (You do not need to prove this.) Determine all pairs of digits ( a,b ) such that 72 b 9 a 2 is divisible by 88. Problem 3 . Use mathematical induction to show that 3 n ≡ 1+2 n 2 (mod 8) for all integers n ≥ 0. Problem 4 . Suppose that a,b ∈ Z and m,n ∈ P . Prove that an ≡ bn (mod mn ) if and only if a ≡ b (mod m ). 1...
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This note was uploaded on 12/28/2010 for the course MATH 135 taught by Professor Andrewchilds during the Fall '08 term at Waterloo.
 Fall '08
 ANDREWCHILDS
 Algebra

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