From the equation you get that y^2 = -1 mod 11 and with properties of the Legendre symbol you quickly find that -1 is a non quadratic residue mod 11 : (-1/11) = -1 because 11 = 3 mod 4
It is a simple and straight question if one knows modulus arithmetic, but if they didn't know that beforehand, it indeed would have required some hard thinking to crack the code. That really shows just how strong of a tool modulus arithmetic is.
From the equation you get that y^2 = -1 mod 11 and with properties of the Legendre symbol you quickly find that -1 is a non quadratic residue mod 11 :
(-1/11) = -1 because 11 = 3 mod 4
taking the equation mod 11 you find that y^2 is -1 mod 11 which is impossible since 11 is a prime that is 3 mod 4.
i was doing y^2 mod 11
It is a simple and straight question if one knows modulus arithmetic, but if they didn't know that beforehand, it indeed would have required some hard thinking to crack the code.
That really shows just how strong of a tool modulus arithmetic is.
i dont really see why the theorem you stated was necessary🤔i must admit it is a quality theorem nonetheless
cool i did the same method
You're asking the viewer if they like math?