Wilson's Theorem and Fermat's Little Theorem Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) Show that is divisible by 11 by grouping together pairs of inverses modulo 11 that occur in

(2) Show that is divisible by 13 by grouping together pairs of inverses modulo 13 that occur in

(3) What is the remainder when is divided by 19?

(4) What is the remainder when 25! is divided by 31?

(5) Using Wilson's theorem, find the least positive residue of modulo 7.

(6) What is the remainder when is divided by 437?

(7) What is the remainder when is divided by 1763?

(8) Using Fermat's little theorem, find the least positive residue of modulo 7.

(9) Using Fermat's little theorem, find the least positive residue of modulo 17.

(10)  Using Fermat's little theorem, solve the linear congruence

(11)  Using Fermat's little theorem, solve the linear congruence and

(12) Show that if is prime then

(13) Show that if is prime then

(14) Show that if is prime and then

• print this page
• pages linking here
• related pages