Find 11⁶⁴⁴ mod 645 Use the following algorithm and show work!

procedure modularExponentiation(b: integer, n = (a_k-1a_k-2...a₁a₀)₂, m:positive integer)

x:= 1

power := b mod m

for i = 0 to k-1

If a_i = 1 then x:= (xpower) mod m

power := (powerpower) mod m

return x ( x equals bⁿ mod m)

Note: in this example m = 645, a_i is the binary expansion of 644, b is 11.

Show all steps to prove that 2^p-1(2^p-1) is a perfect number when 2^p-1 is prime

2^p-1(2^p-1)

Use this definition in problems a and bThe USPS sells money orders identified by an 11 -digit number x₁, x₂, ..., x₁₁. The first ten digits identifies the money order and the

and x₁₁ is a check digit that satisfies the following

x₁₁ = x₁ + x₂ + ... + x₁₀ mod 9.

a. Find the check digit for the money orders that have the

following first ten digits:

a) 7556618873

b) 6966133431

c) 8018937435

d) 3288744134

e) 2378918152

b. Determine if the following are valid or invalid money order

numbers for the USPS.

a) 74051486623

b) 88382013345

c) 56152440784

d) 66806631178

e) 23789181524