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Abstract Algebra

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Moderate

Properties of Euler Phi Function

ABSALG-LKC7VD

Let $p,q$ be distinct primes, and let $\phi$ denote the Euler phi function. Which of the following statements is NOT true?

A

$\phi(pq)=\phi(p)\phi(q)$

B

$\phi(p^2q^3)=\phi(p^2)\phi(q^3)$

C

$\phi(p^4)=p^4-p^3$

D

$\phi(q^3)=\phi(q^2)\phi(q)$