%hw6.tex: Homework assignment 6
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{
\bf Dr. Z.'s Number Theory Homework assignment 6
}

{\bf 1.}: Using the recursive algorithm {\bf directly}, find the proudct-of-prime-powers representation of

{\bf a.} $1000$ {\bf b.} $7007$ {\bf c.} $2700$ {\bf d.} $1024$


{\bf 2.} Use any method to find the  proudct-of-prime-powers representation of

{\bf a.} a googol : $10^{100}$ {\bf b.}: a googolplex $10^{10^{100}}$ 

{\bf c.} 
$$
(3^3 \cdot 5^{101} \cdot 11^{11} ) \cdot (3 \cdot 5^{3} \cdot 11^{12} \cdot 13^{2} \cdot 41^2) \quad .
$$


{\bf 3.} (challenge) Yesterday I went to a bookstore and I overheard a conversation between two people

{\bf A.} This is a nice book, are you going to buy it?

{\bf B.} I like it, since the number in the title is the product of the ages of my three children, can you figure their ages?

{\bf A.} Of course not, there are several possibilities.

{\bf B.} But let me add that all the ages are distinct (i.e. I have neither twins nor a triplet), and their ages is
        at least $2$.

{\bf A.} Yes, now I know the ages of your children.

Can {\bf YOU} figure out their ages?



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