Extra Credit:

$(10$ points$)$

Create a Java project, and call it ExtraCredit. Create a Java main class. This class will have a method

called BinaryModularExponentiation which will accept an array of binary digits, the base number, and

the mod number. This method should apply the binary modular exponentiation algorithm and return the

result to the main method.

Write a method called DecimalToBinary that will convert a decimal number to binary. The main method

will ask the user for a base, an exponent, and a mod number.

$(10$ points$)$

The assignment is to write a java program that calls a function called findA$\_$n$($int n$,$ int a$\_0).$ The first

parameter should be the index in the sequence, and the second parameter should be the initial

condition. Your main$()$ routine should return the result of findA$\_$n$()$ to the console window, and findA$\_$n

should be called $3$ times as follows:

$find{A}_n(5,0)$;

$find{A}_n(5,1)$;

$find{A}_n(5,2)$;

The formula for a$\_$n should be a$\_$n $=4$ a$\_\{$n$-1\}-3.$

The output should be the $5$ th element of the sequence, a$\_\{5\},$ where the initial element is $0,1,$ and $2,$

respectively.

Your function must implement recursion, i$.$e$.$ it must call itself.