The Prime Problem with a One Sentence Proof - Numberphile
More links & stuff in full description below ↓↓↓ A prime number problem posed by Fermat that has been proved multiple times - including a famous proof using ...
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We talk about the two square theorem. This concerns prime numbers. You know, the numbers which are only divisible by 1 and themselves. The question: how to write a prime number as the sum of two squares of natural numbers - of positive natural numbers. The easiest example is: take the prime number 2, the smallest prime number. You can write this as 1 squared plus 1 squared. Let's try the next prime, 3. Well... 1 squared plus 1 squared - obviously not. 1 squared plus 2 squared - already too big, so, no. Argh. 5, 1 squared plus 2 squared. Works. Let's do this Fourth example: 7. You try 1 squared plus... 6, 6 is not a square... 2 squared is 4, plus 3, 3 is not a square. Uh, we see it's not possible. And the question is: Do there exist natural numbers, x and y, su...
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We talk about the two square theorem. This concerns prime numbers. You know, the numbers which are only divisible by 1 and themselves. The question: how to write a prime number as the sum of two squares of natural numbers - of positive natural numbers. The easiest example is: take the prime number 2, the smallest prime number. You can write this as 1 squared plus 1 squared. Let's try the next prime, 3. Well... 1 squared plus 1 squared - obviously not. 1 squared plus 2 squared - already too big, so, no. Argh. 5, 1 squared plus 2 squared. Works. Let's do this Fourth example: 7. You try 1 squared plus... 6, 6 is not a square... 2 squared is 4, plus 3, 3 is not a square. Uh, we see it's not possible. And the question is: Do there exist natural numbers, x and y, su...
