Many problems involve solving an equation with more than one unknown. Such equations are called indefinite or Diophantine equations.
Such problems were dealt with by the most famous mathematicians of antiquity - Pythagoras and Diophantus, and therefore very often, instead of saying that we are solving indefinite equations in integers, we say that we are solving Diophantine equations.
Let's solve this task:
A total of 34 books were sold in a bookstore. A few customers bought 5 books each, and the rest bought 2. At least how many customers did he have in the bookstore?
Solution:
To maximize the number of books a customer has taken, we start with customers buying 5 books each.
The maximum number of people who can buy 5 books each is 34 : 5 = 6 + remainder 4.
This leaves 4 books that can be sold to 2 additional customers buying 2 books each.
Thus, the smallest number of customers who bought books is 8 (6 buying 5 books each and 2 buying 2 books each).
Answer: 8 customers
