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Assume $m=21936520921056942428185744321881874204790829920$ 570235226904516467385564406736567597367535979699930859170 667289061009756151158068196185554149 is a product of two primes $p$ and $q$ and that $\varphi(m)=21936520921056942428185744321881874204$ 790829920570235226904516467385548925092800907044879409345 000125494759694716131857830775913843528947136 . Use these two equations to find the primes $p$ and $q$.

   Assume $m=21936520921056942428185744321881874204790829920$ 570235226904516467385564406736567597367535979699930859170 667289061009756151158068196185554149 is a product of two primes $p$ and $q$ and that $\varphi(m)=21936520921056942428185744321881874204$ 790829920570235226904516467385548925092800907044879409345 000125494759694716131857830775913843528947136 . Use these two equations to find the primes $p$ and $q$.

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Applied Algebra: Codes, Ciphers and Discrete Algorithms

Applied Algebra: Codes, Ciphers and Discrete Algorithms

Darel W. Hardy, Fred… 2nd Edition

Chapter 8, Problem 7

Instant Answer

Step 1

- We are given \( m = pq \) where \( p \) and \( q \) are prime numbers. - We are also given \( \varphi(m) \), which is the Euler's totient function for \( m \). The formula for \( \varphi(m) \) when \( m \) is a product of two distinct primes \( p \) and \( q \) Show more…

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Assume $m=21936520921056942428185744321881874204790829920$ 570235226904516467385564406736567597367535979699930859170 667289061009756151158068196185554149 is a product of two primes $p$ and $q$ and that $\varphi(m)=21936520921056942428185744321881874204$ 790829920570235226904516467385548925092800907044879409345 000125494759694716131857830775913843528947136 . Use these two equations to find the primes $p$ and $q$.

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