Homework due Thursday May 22

1. Read section 4.3 and 4.3 (1,2,3)
2. You can read about the Fermat factorization technique in 4.1. Use this technique to factor 2279, 10541 and 340663.
3. Use Fermat's Little Theorem to show that 9017 and 9991 are composite. That is, find an a such that a^{9016} is not congruent to 1 mod 9017 etc.
4. Practice showing that two sets are equal. All the sets here are infinite so to show that S=T you must show that all elements in S are contained in T and all elements in T are contained in S.
   1. Let S= { 3s+5t for all integers s and t } and let T= Z = all integers = { ...-2,-1,0,1,2, ... }.Show S=T. Hint: to show S is contained in T you must show every element of S is an integer. To show T is contained in S, first show 1 is in S then use that to help you show all integers are in S.
   2. Let S= { 6s+8t for all integers s and t } and let T= 2Z = all even integers = { ...-4,-2,0,2,4, ... }.Show S=T.
5. Bonus Problem: 4.3 number 5
6. Study for QUIZ NUMBER THREE