what is the differnce in a grapich when I use (mod p), for example the difference between y=x and y=x (mod 3)

Question

I'm studying elliptic curve criptography,in partocular secp256k1 for used in bitcoin-core,and it uses the mod p. strong text

Answer 1

When you try to find mod 3 of a number, you are essentially trying to find the remainder of the number when you divide it by 3. (eg. 38 mod 3 == 3(12) + 2 mod 3 == 2)

When you graph y = x, you should get the standard graph that you learn in algebra 1. When you graph y = x mod 3, you should get have a cycle where y increases from 0 to 3, and then reset back to 0 (every 3)