Question

Assume $$ m=25972641171898723 $$ is a product of two primes $p$ and $q$ and that $$ \varphi(m)=25972640809676568 $$ Use these two equations to find the primes $p$ and $q$.

   Assume
$$
m=25972641171898723
$$
is a product of two primes $p$ and $q$ and that
$$
\varphi(m)=25972640809676568
$$
Use these two equations to find the primes $p$ and $q$.

Applied Algebra: Codes, Ciphers and Discrete Algorithms

Applied Algebra: Codes, Ciphers and Discrete Algorithms

Darel W. Hardy, Fred… 2nd Edition

Chapter 8, Problem 4

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Step 1

We are given that \( m = p \times q \) where \( p \) and \( q \) are prime numbers, and \( m = 25972641171898723 \). We are also given \( \varphi(m) = 25972640809676568 \), where \( \varphi \) is the Euler's totient function. Show more…

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Assume $$ m=25972641171898723 $$ is a product of two primes $p$ and $q$ and that $$ \varphi(m)=25972640809676568 $$ Use these two equations to find the primes $p$ and $q$.

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