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An abstract algebra teacher intended to give a typist a

Chapter 2, Problem 21E

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QUESTION:

An abstract algebra teacher intended to give a typist a list of nine integers that form a group under multiplication modulo 91. Instead, one of the nine integers was inadvertently left out, so that the list appeared as 1, 9, 16, 22, 53, 74, 79, 81. Which integer was left out? (This really happened!)

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QUESTION:

An abstract algebra teacher intended to give a typist a list of nine integers that form a group under multiplication modulo 91. Instead, one of the nine integers was inadvertently left out, so that the list appeared as 1, 9, 16, 22, 53, 74, 79, 81. Which integer was left out? (This really happened!)

ANSWER:

Step 1 of 2

Write the subset  as:

                                                 

According to given condition  is a group under multiplication modulo 91. We have to determine the value of .

 

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