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1. Find the value of the Euler phi-function for each of the following integers a) 100 b) 256 c) 1001 d) 2-3-5-7-11-13 e) 10! f) 20!.

1. Find the value of the Euler phi-function for each of the following integers a) 100 b) 256 c) 1001 d) 2-3-5-7-11-13 e) 10! f) 20!.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Exercise: Calculating the Euler Phi-Function** Find the value of the Euler phi-function for each of the following integers: a) 100 b) 256 c) 1001 d) \(2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13\) e) \(10!\) f) \(20!\) This exercise asks you to compute the Euler phi-function, which is significant in number theory because it gives the count of integers up to a given integer that are coprime with it.
Transcribed Image Text:**Exercise: Calculating the Euler Phi-Function** Find the value of the Euler phi-function for each of the following integers: a) 100 b) 256 c) 1001 d) \(2 \cdot 3 \cdot 5 \cdot 7 \cdot 11 \cdot 13\) e) \(10!\) f) \(20!\) This exercise asks you to compute the Euler phi-function, which is significant in number theory because it gives the count of integers up to a given integer that are coprime with it.
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Euler Phi-Function: Let n>1 be an integer and the prime factorization is n=p1k1·p2k2···pnkn, then the Euler Phi-Function of n is number of non-negative integers less than n that are relatively prime to n. Denoted by ϕ(n) and which is given by:

ϕn=n·1-1p1···1-1pn

 

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