The Fundamental Theorem of Arithmetic

The first famous mathematical theorem that I became acquainted with is not the Pythagorean theorem, but rather the Fundamental Theorem of Arithmetic. This theorem states that every positive integer can be uniquely expressed as a product of prime factors. Do not underestimate this theorem; it is rightfully called a "fundamental theorem" because it reveals a fundamental property of numbers, which serves as a fundamental tool for mathematicians.

 

Let me give you an example to illustrate its usefulness: "If we divide 169 candies equally among a group of children, and each child receives more than one candy, what is the number of children in the group?" Can you solve it?

 

The answer is 13. Why? The key lies in realizing that the prime factorization of 169 is 13 × 13!

 

Now, let me pose a question for you: If A × (B + C) = 209, where A, B, and C are prime numbers, and B > C, can you find the values of A, B, and C?