Let $\phi$ denote Euler's totient function, and $p, q > 1$ be primes. Conjecture and prove a formula for $\phi(pq)$ in terms of $p$ and $q$.

Question

Let $\phi$ denote Euler's totient function, and $p, q > 1$ be primes. Conjecture and prove a formula for $\phi(pq)$ in terms of $p$ and $q$.
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Solution 1

Sure, here is the conjecture and proof:

Conjecture: For any two primes p and q, the Euler's totient function φ(pq) = (p-1)(q-1).

Proof:

By definition, Euler's totient function φ(n) counts the positive integers less than n that are relatively prime to n.

Since p and q are primes, they have no co Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

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