AFM101 Lecture Notes - Lecture 7: Prime Number, Mathematical Induction

• School: University of Waterloo
• Department: Accounting & Financial Management
• Course: AFM101
• Professor: Grace Loney

Document Summary

An integer a = anan 1 . a2a1a0 is divisible by 11 if and only if its alternating sum of digits a0 a1 + a2 a3 + + ( 1)nan is divisible by 11. We rst notice that 1 away of any power of 10 there is always a multiple of 11. Indeed, integers with an even number of digits, all of which are equal to 9, are divisible by 11, so if we subtract 1 from an even power of 10 we get a multiple of 11. 01 with an even number of zeroes between the two 1s are also divisible by 11. That is, if we add 1 to an odd power of 10 we get a multiple of 11. We will use this in the argument below. Let a = anan 1 . a2a1a0 , where a0, a1, . A = a0 + a1 10 + a2 100 + a3 1000 + + an 10n.