Sums of 2 Squares (Fermat's Christmas Theorem)

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Explanations 5

Q2,P1Q_2, P_1Q2,P1 and P3P_3P3 : The Definition So, let's take a look at what Q2,P1Q_2, P_1Q2,P1 and P3P_3P3 are. P1P_1P1 and P3P_3P3 Well, P1P_1P1 is the set of all pr…
By Zi Song Yeoh, Alex Federspiel, Victor Wang
Q2,P1Q_2, P_1Q2,P1 and P3P_3P3 : Some Simple Properties Previous part In this article, we'll look at the respectively properties of these sets. P3P_3P3 We know that the set …
By Zi Song Yeoh, Alex Federspiel, Victor Wang
Q2,P1,P3Q_2, P_1, P_3Q2,P1,P3 : Similarities and Differences Previous part So, we've introduced three seemingly bizarre sets. Now what? We'll prove two statements in this art…
By Zi Song Yeoh, Alex Federspiel, Victor Wang
Q2,P1Q_2, P_1Q2,P1 and P3P_3P3 : The complete characterization of Q2Q_2Q2 Previous part In this article, we'll completely characterize which numbers can be written as the su…
By Zi Song Yeoh, Victor Wang
Recall that in Z[n]\mathbb{Z}[\sqrt{n}]Z[n], N(α)=a2−nb2N(\alpha)=a^2-nb^2N(α)=a2−nb2. What if nnn was −1-1−1, so that we are working in Z[i]\mathbb{Z}[i]Z[i]? What are the pos…
By Jason Chen