Understanding the Two Square Theorem

The video discusses the two square theorem, which involves expressing prime numbers as the sum of two squares. It explains the criterion for determining if a prime can be expressed this way, based on divisibility by 4. The video also covers the historical context, including Fermat's initial observations and subsequent proofs by mathematicians like Euler, Gauss, and Dedekind. The video concludes with a mention of Don Zagier's one-sentence proof.

What is the smallest prime number that can be expressed as the sum of two squares?

• 2

• 3

• 7

• 5

Which of the following statements is true about finding a formula for expressing large primes as the sum of two squares?

• No formula exists.

• A formula exists but is complex.

• A formula exists but is not yet discovered.

• A formula exists for small primes only.

Who was the first mathematician to explore the problem of expressing primes as the sum of two squares?

• Dedekind

• Gauss

• Euler

• Fermat

According to Fermat's rule, a prime number can be expressed as the sum of two squares if:

• It is even.

• It is one less than a multiple of 4.

• It is a perfect square.

• It is divisible by 3.

What is the result when you subtract 1 from the prime number 17, according to Fermat's rule?

• 16

• 15

• 18

• 19

Which mathematician provided the first proof of Fermat's theorem?

• Dedekind

• Gauss

• Zagier

• Euler

How many years after Fermat did Euler provide a proof for the theorem?

• 50 years

• 100 years

• 200 years

• 150 years

Which mathematician is known for providing a one-sentence proof of Fermat's theorem?

• Zagier

• Euler

• Gauss

• Dedekind

What is the significance of Don Zagier's proof?

• It was the longest proof.

• It was a one-sentence proof.

• It was the most complex proof.

• It was the first proof.

Why do mathematicians provide different proofs for the same theorem?

• To shed different light on the theorem.

• To show off their skills.

• To make the theorem more complex.

• To confuse students.