Write c++ programs that implement the exhaustive method for proofs.

a. Prove that 3x2 + 4y2 = 271 has positive integer solutions in x and y. To do this with programming, you only need to write a program to find the integer solutions. Please print out in the console the found solutions for x and y.

b. Write a program to prompt users to input an integer n. Prove or disprove the statement that there are positive integer solutions in x and y such that 3x2 + 4y2 = n. Print out in the console that There is an integer solution in x and y, and the solution is (YourFoundX, YourFoundY) if the statement is true; otherwise, print out in the console that There are no integer solutions and the range of x that is searched is (1, YourUpperBound). (Note that you need do some simple calculations to make YourUpperBound as tight as possible.).