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Prove or disprove: There exist distinct integers a, b, c 2 such that a b (mod c), b c

Chapter 7, Problem 18

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QUESTION:

Prove or disprove: There exist distinct integers a, b, c 2 such that a b (mod c), b c (mod a) and c a (mod b).

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QUESTION:

Prove or disprove: There exist distinct integers a, b, c 2 such that a b (mod c), b c (mod a) and c a (mod b).

ANSWER:

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The objective of the question is to identify that whether for three distinct integers that are greater than 1, a identical to b space open parentheses m o d space c close parentheses comma space b identical to c space open parentheses m o d space a close parentheses comma space a n d space c identical to a space open parentheses m o d space b close parentheses holds. The condition a identical to b open parentheses m o d space c close parentheses holds if a space m o d space c space equals space b space m o d space c

 

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