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Chapter 1: Q21E (page 49)

How many integers modulo113 have inverses?(Note:113=1331)

Short Answer

Expert verified

The number of integers coprime to113 are 1210

Step by step solution

01

Explain Inverse modulo

The modular multiplicative inverse can be defined as the GCD(a,b)must be equal to 1 and a, b are relatively prime.

02

Calculate the number of integers

Consider that the numbers1,11,121,1331 are the factors of 113. It is given that 113=1331, the number of integers can be calculated as follows,

113-1-112-1=1331-1-121-1=1330-120=1210

Therefore, The number of integers coprime to 113 are 1210

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