Give the exact number of additions performed in the following segment of certain algorithm assuming a₁, a2,..., an are positive real numbers and n = 11 for i=1 to n for j=1 to n Sij = aj + aj + 2;

А5. a) How many terms are there in the following Geom etric Progression? 2, 4, 8, ... 1024. b) Write an algorithm to find whether a given number is odd or even.

4. Find the gcd of 182 and 1001 by Euclidean Algorithm, and find integers m, n such that the gcd equals 182m + 1001n.

1.9. Use the Euclidean algorithm to compute the following greatest common divi- sors. (a) gcd (291, 252). (b) gcd(16261, 85652). (c) gcd(139024789, 93278890). (d) gcd(16534528044, 8332745927). 1.10. For each of the gcd(a, b) values in Exercise 1.9, use the extended Euclidean algorithm (Theorem 1.11) to find integers u and v such that au + bv = gcd(a, b).

Q10. Consider the following algorithm: 81 = 4 82 = 9 For k starting at 3 and ending with 8: Sk = (k-1).gk-1 + gk-2 What is the last term, gg, of the recursive sequence generated as a result of executing this algorithm?

1.30. For each of the following primes p and numbers a, compute a-¹ mod p in two ways: (i) Use the extended Euclidean algorithm. (ii) Use the fast power algorithm and Fermat's little theorem. (See Example 1.28.) (a) p = 47 and a = 11. (b) p= 587 and a = 345. (c) p = 104801 and a = 78467.

do fast i will 5 upvotes.

6. Trace Algorithm 4 when it is given m = 7, n = 10, and b = 2 as input. That is, show all the steps Algorithm 4 uses to find 2¹0 mod 7.

Find all integer values of x for which 3x = 4 (mod 8).

Solve for d, 19d ≡ 1 mod (37422000) using the "Extended Euclid's Algorithm"