Let's solve a quadratic equation in Zp, where p is prime. We cannot use thequadratic formula, because we cannot define a square root in Zp. However, wecan still try to complete the square.Specifically, consider the quadratic equation y^2 y - 11 = 0 in Z41.(a) Solve the equation 2a = 1 in Z41.(b) Find elements a, b ∈ Z41 such that y^2 y - 11 = (y a)^2 - b in Z41.(c) Use (b) and Question 3(b) to write down the solution(s) of y^2 y - 11 = 0in Z41.
Let's solve a quadratic equation in Zp, where p is prime. We cannot u…
Mar 6, 2024
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