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This quiz consists of 5 multiple choice and 5 short answer questions through A Sampler of Euler's Number Theory.

## Multiple Choice Questions

**1. Who was Euler's teacher?**
**(a)** Isaac Newton. **(b)** Jakob Bernoulli. **(c)** Johann Bernoulli. **(d)** Gottfried Leibniz.

**2. Which of the following becomes an important definition in mathematics that was first presented in Elements?**
**(a)** Circle. **(b)** Parallel line. **(c)** Intersection. **(d)** 180 degree angle.

**3. What did Euler prove about 2²ⁿ + 1?**
**(a)** That the statement is always a prime number. **(b)** That the statement is neither prime nor composite. **(c)** That the statement is always a composite number. **(d)** That the statment is sometimes prime and sometimes composite.

**4. What great theorem is presented by Dunham in this chapter?**
**(a)** A theorem on infinite series published by Jakob Bernoulli. **(b)** A theorem on series developed by Jakob and published by Johann Bernoulli. **(c)** An improvement on Leibniz's caluclus as presented by Jakob Bernoulli. **(d)** A theorem on finite series developed by Johann Bernoulli.

**5. Which of the following was an important proposition given by Euclid's number theory?**
**(a)** Any perfect number is divisible by some composite number. **(b)** Any even number is divisible by 3. **(c)** Any composite number is divisible by some prime number. **(d)** Numbers from one to ten are only divisible by composite numbers.

## Short Answer Questions

**1.** Which of the following was NOT a field in which Isaac Newton made enormous advances?

**2.** What didn't Euler attempt?

**3.** Numbers whose divisor add up to itself, was considered which type of number according to Euclid?

**4.** What range of values did Archimedes determine for pi?

**5.** How did Archimedes demonstrate his theory of pi?

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