%hw15.tex: Homework assignment 15
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{
\bf Dr. Z.'s Number Theory Homework assignment 15
}

{\bf 1.} Using the definition, find 

{\bf a.} $\phi(16)$ \quad, \quad {\bf b.} $\phi(12)$  \quad .


{\bf 2.} Using the formula, find 

{\bf a.} $\phi(1001)$ \quad, \quad  {\bf b.} $\phi(1000)$ \quad, \quad  {\bf c.} $\phi(10^{100})$ (leave it factored) \quad .


{\bf 3.} Verify Euler's Classical Formula for 

{\bf a.} $n=14$ \quad , \quad  {\bf b.} $n=70$ .


{\bf 4.} State and prove the multiplicative property  for $\phi(n)$

{\bf 5.} State and prove the formula for Euler's Totient Function.

{\bf 6.} State and prove Euler's Classical Formula for the divisor-over-divisors of $n$ of $\phi$.




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