Let $p$ and $q$ be different prime numbers. How many divisors does the number have:
a) $p q$;

b) $p^{2} q$

c) $p^{2} q^{2}$

d) $p^{m} q^{n}$?
г) Each divisor also has the form $p^{k} q^{l}$, and the exponent $k$ can be chosen in $m+1$ ways (from 0 to $m$), while the exponent $l$ can be chosen in $n+1$ ways.

## Answer

a) 4 divisors;
b) 6;
c) 9;
d) $(m+1)(n+1)$ divisors.

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