# Homework Assignment #2

## Objective

To gain experience with modular exponentiation.

## Exercises

Show all work. i.e., justify your answers.

### Question 1

1.25 in the textbook using modular exponentiation.

Be careful to use the congruence relation symbol ($\equiv$) properly. In particular, don't use the equals sign (“=”) when you should use congruence. (Note that you can type that symbol in Microsoft Windows by holding the ALT key and typing 240 on the number pad.)

If you're still having trouble distinguishing the congruence relation from equality, here's a little tutorial that may be helpful to you: http://www-cs-students.stanford.edu/~dalewis/congruent.html

### Question 2

Compute $2^{126}$ (mod 127) using any valid method.

### Question 3

Implement modular exponentiation in C#. Indicate on your homework assignment that you have done so.

(This gives you a head-start on project #1.)

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