Q1. (5 points) Consider Z, where p is prime. Prove that [x][x] = [y][y] if and only if [x] = [y] or [x] = [-y]. Hint: Sh

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Q1 5 Points Consider Z Where P Is Prime Prove That X X Y Y If And Only If X Y Or X Y Hint Sh 1 (14.97 KiB) Viewed 31 times

Q1. (5 points) Consider Z, where p is prime. Prove that [x][x] = [y][y] if and only if [x] = [y] or [x] = [-y]. Hint: Show that ([x] + [y]) ([x] - [y]) = [x][x]-[y][y], then use it. Or alternatively, note that the statement is equivalent to ² = y² (mod p) if and only if a = y (mod p) or x = -y (mod p).