Homework 10:
Exercise 1. Do the exercises 8.6, 8.7, 8.8 in the textbook.
Exercise 2. A common divisor of m and n is an integer that divides both m and n. The greatest common
divisor, written ๐๐๐โก(๐, ๐), is the largest common divisor of m and n. Write a function to find the
greatest common divisor (gcd) of two numbers in two ways (recursive and not recursive).
Exercise 3. BEZOUTโS THEOREM: If a and b are positive integers, then there exist integers s and t such
that gcd(a, b) = sa + tb. Write a function to find s and t.
Exercise 4. Write a function to determine if a number is the product of two primes.
(hint: if ๐ = ๐ ร ๐, check_prime(p) and check_prime(q)โฆ).
Exercise 5. a) Write the funtion ๐๐๐๐(๐, ๐) to get a random number in [0; ๐]. The function defined by
๐๐๐๐(๐, ๐ )=(7 โ ๐๐๐๐(๐ โ 1, ๐)+ 1) mod ๐,
Where a seed ๐๐๐๐(0, ๐) = s (import time
s = time.time()).
b) Write function shuffle(alist) to shuffle items in alist.
(Hint: swap alist[i] and alist[rand(i,n)])
Exercise 6. Write a function to calculate (c**s)%z where
๐โก = โก1136503834252139, ๐ = 2413713104313437โก๐๐๐โก๐ง = โก3017141490284017.