For which of the following problems there exists an efficient algorithm to solve it? i. Computing Euler's Totient function without knowing prime factorization ii. Factoring large numbers iii. Computing discrete logarithms iv. All of the above v. None of the above

Discrete math problem: Is the set of odd negative integers finite, countably infinite, or uncountable? If it is countably infinite, exhibit a one-to-one correspondence between the set of positive integers and that set.

Discrete math

Question 4: Use a proof by contradiction to prove that the sum of an irrational number x and a rational number y is irrational.

Solve the following nonlinear equations by Newton iteration and fixed point with initial conjecture x, = yo = 1.2. And get the answer using Python code with an accuracy of 3 significant digits. Sy = -x² +x + 0.75 ly + 5xy = 22 %3D

Discrete Math

InstructionsSolve for the following problems numerically using Manual solutions and using Python Code (Numpy)Question 2. Prove the equality of the following trigonometric functions using Euler identities. Furtherprove the equality in Python. Furthermore, plot the left-hand side and right-hand side of the equation andtheir Euler forms as additional proof.

Question 14 For the point P=(11,3) on the elliptic curve given by y = x° +2x +5mod19, calculate 4 P. *Un.. O Revi. R. Inbo... search hp 16 10 & *- 6. 7. 8.

Use the Master Theorem to solve the following recurrence equation. DETAILED steps and proofs are required.   T(n) = 9T(n/3)+37n2