Let E : y2 = x3 + 3x + 4 be an elliptic curve over F37. (a) Find all the elements of the elliptice curve group. (b) Find the order of the group. (c) Find a primitive element of this group and call it G. (d) Compute [30]G = G ⊕ G ⊕ · · · ⊕ G (addition of 30 many G’s)   kindly help with full explanation. Thank you!

PLEASE DO Q4 IN PYTHON

IN PYTHON I want a code in python and no need to post work on paper Iwant a screenshot of the code A tridiagonal matrix is one where the only nonzero elements are the ones on the main diagonal and the ones immediately above and below it.Write a function that solves a linear system whose coefficient matrix is tridiag- onal. In this case, Gauss elimination can be made much more efficient because most elements are already zero and don't need to be modified or added. As an example, consider a linear system Ax = b with 100,000 unknowns and the same number of equations. The coefficient matrix A is tridiagonal, with all elements on the main diagonal equal to 3 and all elements on the diagonals above and below it equal to 1. The vector of constant terms b contains all ones, except that the first and last elements are zero. You can use td to find that x1= −0.10557. The following code format should help: def td(l, m, u, b):   '''Solve a linear system Ax = b where A is tridiagonal      Inputs: l,…

5. Find a closed form representation for the function defined recursively by f(0) = 5 and f(n+1)=2f(n)+4". Prove that your representation is correct using an inductive argument.

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(e) Give a simple recursive definition for the function sos(A), which gives the length of the shortest oscillating supersequence of an arbitrary array A of integers.