a) Prove that 10" =+1 (mod 11) for any n EN. b) Suppose the integer r has digits rI-1I, I0. Prove that r=0 (mod 11) if and only if o(-1)'r, = 0 (mod 11). c) Is 135802469132 is divisible by 11? Explain why.
a) Prove that 10" =+1 (mod 11) for any n EN. b) Suppose the integer r has digits rI-1I, I0. Prove that r=0 (mod 11) if and only if o(-1)'r, = 0 (mod 11). c) Is 135802469132 is divisible by 11? Explain why.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.5: Congruence Of Integers
Problem 30E: 30. Prove that any positive integer is congruent to its units digit modulo .
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