1. Prove that the algorithm is partially correct. To do so, show that as when and are reassigned in each iteration of the loop their greatest common divisor does not change. 2. Show that the loop iterates times. (HINT: prove that decreases by at least of its prior value in each iteration of the loop). 3. Make an argument for full correctness that does not involve explicitly adding a proof of termination.

Create a console project in c#. 1. create an interface "imyinterface.cs" - add a method "string imessage()" 2. create a class named "c1.cs" - add 4 private data members, create property for each data member double loanamnout=0.0; double years=0.0; double interests=0.0; double interestrate=0.0; 3. - add a constructor with parameters to assign values to loanamnout, years, interestrate with values that user entered. 4. - add one method “payinterests()” to return the interests interests = loanamnout * interestrate * years 5. - inheritate "imyinterface", implement the method " imessage()", return string "be ready! ” 6. in program.cs, have users to enter loanamnout, years, interestrate. - call method payinterests() to display total interests. - call imessage() to display "be ready! ”