A woman took a certain number of eggs to market and sold some of them.  
The next day, through the industry of her hens, the number left over had
been doubled, and she sold the same number as the previous day.  On the
third day the new remainder was trippled, and she sold the same number as
before.  On the fourth day the remainder was quadrupled, and her sales the
same as before.  On the fifth day what had been left over were quintupled,
yet she sold exactly the same as on all the previous occasions and so
disposed of her entire stock.

What is the smallest number of eggs she could have taken to the market the
first day, and how many did she sell daily?