Compute 13^-1 (mod 19) using Fermat Little Theorem. Show all work/proof
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Compute 13^-1 (mod 19) using Fermat Little Theorem. Show all work/proof
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- Use the Time-Hierarchy Theorem to prove that P!= EXP.Show the distance matrix D(k) for 0 ≤ k ≤ n that results from applying the Floyd-Warshall algorithm for the graph shown in Figure 3.Find 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
- 1. In order to understand that Gaussian or Eisenstein integers have a unique decomposition in terms of prime (G/E) integers, it has to be understood that the decomposition can differ only by __________________ and ____________. 2. For example, for the Gaussian integer 5, i.e., 5 + 0i, the decomposition 5=(1+2i)(1−2i) and the decomposition 5=(2+i)(2−i) look different, but their difference can be resolved by noticing that each factor in the expression (1+2i)(1−2i) is a rearrangement of the factors in the expression (2+i)(2−i) after multiplying by the appropriate unit. That is, (1+2i)=u⋅(2−i), where the unit u = _____ and (1−2i)=v⋅(2+i), where the unit v = _____.Find the space complexitySolve this recurrence relations together with the initialconditions given. a_{n+2} = −4a_{n+1} + 5a_n for n ≥ 0, a_0 = 2, a_1 = 8
- To prove that the Chandy-Lamport algorithm passes the safety condition, demonstrate that it does.Use the Euclidean algorithm to find the GCD of the following pairs of integers. Also find s and t such that as+bt=gcd(a,b). (a) a=2938 and b=183 (b) a=93182 and b=246 Show all calculations. Does a inverse mod b exist? If yes, what is it.Analyze the following recurrences and show their time complexity functions using (1) iteration method and (2) Master Theorem.