# PreTeXt Sample Book: Abstract Algebra (SAMPLE ONLY)

## Exercises5.9Parsons Exercises

### 1.Parsons Problem, Mathematical Proof.

Create a proof of the theorem: If $$n$$ is an even number, then $$n\equiv 0\mod 2\text{.}$$
Hint.
Dorothy will not be much help with this proof.

### 2.Parsons Problem, Programming.

The Sieve of Eratosthenes computes prime numbers by starting with a finite list of the integers bigger than 1. The first member of the list is a prime and is saved/recorded. Then all multiples of that prime (which not a prime, excepting the prime itself!) are removed from the list. Now the first number remaining in the list is the next prime number. And the process repeats.
The code blocks below can be rearranged to form one of the many possible programs to implement this algorithm to compute a list of all the primes less than $$250\text{.}$$ [Ed. this version of this problem requires the reader to provide the necessary indentation.]
This reprises Exercise 2.5.1.

### 3.Parsons Problem, Programming.

The Sieve of Eratosthenes computes prime numbers by starting with a finite list of the integers bigger than 1. The first member of the list is a prime and is saved/recorded. Then all multiples of that prime (which not a prime, excepting the prime itself!) are removed from the list. Now the first number remaining in the list is the next prime number. And the process repeats.
The code blocks below can be rearranged to form one of the many possible programs to implement this algorithm to compute a list of all the primes less than $$250\text{.}$$ [Ed. this version of this problem does not require the reader to provide the necessary indentation, which is the default.]
This reprises Exercise 2.5.1.

### 4.Parsons Problem, Mathematical Proof, Numbered Blocks.

Create a proof of the theorem: If $$n$$ is an even number, then $$n\equiv 0\mod 2\text{.}$$ [Ed. This version has numbered blocks, online they are on the right end of the block.]
Hint.
Dorothy will not be much help with this proof.

### 5.Parsons Problem, Programming.

The Sieve of Eratosthenes computes prime numbers by starting with a finite list of the integers bigger than 1. The first member of the list is a prime and is saved/recorded. Then all multiples of that prime (which not a prime, excepting the prime itself!) are removed from the list. Now the first number remaining in the list is the next prime number. And the process repeats.
The code blocks below can be rearranged to form one of the many possible programs to implement this algorithm to compute a list of all the primes less than $$250\text{.}$$ [Ed. This version has numbered blocks, online they are on the left end of the block.]
This reprises Exercise 2.5.1.