# SICP Solutions

### Section - 2.1 - Introduction to Data Abstraction

#### Exercise 2.5

We have to show that any pair of non-negative integers, $a$ and $b$, can be represented using a single integer: $2^a 3^b$.

Since any number can be represented as a product of a unique combination of prime numbers, it follows that any number $2^a 3^b$ will result in a unique number i.e. no other number will have same combination of $2$ and $3$.

Thus we can get back the pair $(a,b)$ using the number $2^a 3^b$. To get back the pair we need to find the number of times we can divide the number by $2$ and $3$ to get $a$ and $b$ respectively.

Output: