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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. Which of the following could NOT be included as a step in Euclid's great theorem?**
**(a)** If a new number is found to be composite, then it must have some prime as a divisor. **(b)** After summation, the new number can be prime or composite. **(c)** Take a finite group of primes and add them together, plus one. **(d)** Divide a infinite group of primes by the sum of their composites.

**2. In the Bernoulli's time, what was the current definition of a series?**
**(a)** The sum of a finite series of terms. **(b)** The infinite sum of a convergent series. **(c)** The finite sum of a divergent series. **(d)** The sum of a never-ending series of terms.

**3. According to Euclid, when is a triangle a right triangle?**
**(a)** When a triangle has three sides whose squares are equal to the area of the triangle. **(b)** When a triangle does not have a side which can be considered a hypotenuse. **(c)** When a triangle can be constructed with three unequal sides. **(d)** When a triangle has a side whose square is the sum of the squares of the two legs.

**4. Who was the author of the book Elements?**
**(a)** Einstein. **(b)** Lindemann. **(c)** Hippocrates. **(d)** Euclid.

**5. Which of the following did Dunham concentrate on as one of Newton's great advances?**
**(a)** Quintic theorem. **(b)** Area of a sphere. **(c)** Binomial theorem. **(d)** Quadratic equation.

## Short Answer Questions

**1.** What does the Pythagorean Theorem state?

**2.** Which of the following can not be solved using algebra?

**3.** What did Dunham consider extraordinary about the Elements?

**4.** What did Newton's calculus involve?

**5.** Where was Neil's Abel from?

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