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{\bf Correction to Spring 1997 Practice Final Question 5}
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Answer {\bf T} or {\bf F}:
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\begin{list}{{\bf T\ \ F\ \ \ }}{\setlength{\leftmargin}{40pt}%
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\item[{\bf True}]
The mapping $f_a:Z_p \rightarrow Z_p$ defined by
\[ f_a(x) = ax \pmod p\]
is a bijection for any nonzero $a\in Z_p$, when $p$ is prime.
\item[{\bf False}]
For all $a,b$ in $\naturals$, $\gcd(a^2b,ab^2) = ab$.
\item[{\bf True}]
If $a^{-1}$ (mod $b)$ exists, then
so does $b^{-1}$ (mod $a)$.
\item[{\bf False}]

Let $\lambda(n)$ denote the number of distinct prime factors
of $n$.  Then $\lambda(n) = \Omega(\mbox{lg lg } n)$.
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