Determine how many times the innermost loop will be iterated when the following algorithm segment is implemented and run. (Assume that  a, b, c, and d  are positive integers. Assume  a ≤ b and c ≤ d.) for i := a to b     for j := c to d         [Statements in body of inner loop.           None contain branching statements that           lead outside the loop.]     next j next i

Let d = (4087, 4757). Writed as a linear combination of 4087 and 4757, and find the multiplicative inverse of 4087/d modulo 4757/d. Show all work.

Give a recurrence relation that would fit the sequence a1, az, A3, A4, A5, .= 1,2, 5, 26, 677 ...

Write a recurrence relation and initial conditions for the number Sn of sequences of Nickles, dimes and quarters that can be inserted into a vending machine to purchase a soft drink costing 5n cents. How many sequences are there for a drink costing 50 cents?

Find a recurrence relation for the number of sequences of yellow and purple stones of length N, where each sequence has the property that no two adjacent stones are purple. HINT: Treat sequences whose final stone is yellow separately from sequences whose final stone is purple.

Suppose that you start browsing the internet on a specified page c. Let x be all the websites you can reach by following links, starting at x. Give a reccursive defintion for the set x including both the recursive part and the base case.