Give the exact number of multiplications performed in the following segment of an algorithm assuming a₁, a2,..., an are positive real numbers and n = 13. for i=1 to n for j=i+1 to n tij =iaj;

If you are using the Sieve of Eratosthenes to find all the prime numbers between 50 and 150, how many times are you going to perform the algorithm before you can con- clude that all the numbers which remains un-striken are prime numbers. 12 2 O 11

(2) Let a = 218 and b =-115. Use the Euclidean Algorithm to find the gcd(a,b) and integers m and n such that gcd(a,b)=ma+nb .

1. For each pair of integers m and n, use the division algorithm to divide m by n. Write the result in the form m = q⋅n + r where 0 < r < n. a. m = 32 and n = 9 b. m 62 and n = 7 = c. m -45 and n = 11 d. m 3 and n = 8 2. For each pair of integers a and b, use the Euclidean Algorithm to find the GCD(a, b). Then use Theorem 92 to find the LCM(a, b) a. a = 48 and b = 54 b. a = 330 and b = 156 c. a=1188 and b = 385 3. For each pair of integers m and d, calculate m mod d. Show your work! a. m 43 and d = 9 b. m 50 and d = 7 c. m 28 and d = 5 d. m = 30 and d = 2