Did you guys know that the Quadratic Reciprocity law….

”was conjectured by Euler and Legendre and first proven by Gauss. He refers to it as the 'fundamental theorem' in the Disquisitiones Arithmeticae and his papers; privately he referred to it as the 'golden theorem'. He published six proofs, and two more were found in his posthumous papers. **There are now over 200 published proofs!**underline text “

That is a lot of proofs for one law! I wanted to know more about these proofs so I did some more researching and found that:

”Of relatively elementary, combinatorial proofs, there are two which apply types of double counting. One by Ferdinand Eisenstein counts lattice points. Another applies Zolotarev's lemma to Z/pqZ expressed by the Chinese remainder theorem as Z/pZ×Z/qZ, and calculates the signature of a permutation.”

As of now, I do not understand these proofs at all. We will probably learn about them soon I am sure. I guess this is just a little preview then!