Find the inverse s of -1959 modulo 979 such that 0 ≤ s < 979. You must show all the detailed steps.
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Q: 1. Find the inverse s of -1959 modulo 979 such that 0 < s< 979. You must show all the detailed…
A: To calculate mod inverse of -1959 mod 979.
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- Solve this recurrence relations together with the initialconditions given. a_{n+2} = −4a_{n+1} + 5a_n for n ≥ 0, a_0 = 2, a_1 = 8Simplify the following expression using K-Maps (1) sum of the products and (2) products of sums: F(A,B,C,D)=BD′+B′CD+ABC+ABC′D+B′D′(a) Given a DFA M = (Q, Σ, δ, q0, F), consider M' = (Q, Σ, δ, q0, F'), where F' = Q − F. Prove that L(M') is the complement of L(M). (b) Give a counter-example to show that the above construction with NFAs does not (always) yield the complement.
- Show that (p ∧ q) → r and (p → r) ∧ (q → r) are not logically equivalent, without using truth tables.evaluate nCxpxqn-x for the values of n, x, and p given in Problem A) n= 4, x= 2, p=1/2Find the multiplicative inverse of (x6 + x3 + 1) in GF(28) mod x8 + x4 + x3+ x + 1 using the extended Euclidean algorithm. Attach a screenshot that show all the intermediate steps to derive your answer.
- Show that StartFraction d Over dx EndFraction (ln kx)equalsStartFraction d Over dx EndFraction ln x, given that xgreater than 0 and kgreater than 0 is a real number.Using limit, compare the order of the growth of functions. 1-2n&6n 2-log2n &n3 3-100n3& log2n n2and 4nFind the value of x for the following sets of congruence using the Chinese remainder theorem.a. x ≡ 2 mod 7, and x ≡ 3 mod 9b. x ≡ 4 mod 5, and x ≡ 10 mod 11c. x ≡ 7 mod 13, and x ≡ 11 mod 12
- Let R=ABCDEGHK and F= {ABK→C, A→DG, B→K, K→ADH, H→GE} . Is it in BCNF? Prove your answer.Prove that for all integers a, b, and c, with a ̸= 0, if a|b and a|c, then a|(bx + cy).List the 4 Chebyshev interpolation nodes in the interval [0, 1] Hence, use the nodes to construct an interpolating polynomial for the function: f(x) = x ln(x + e^x)