SET A Proofs (5 points each) Prove that the sum of two odd integers is even. Prove that every prime number greater than 3 is either one more or one less than a multiply of 6. Prove: If n^2 is not divisible by 5, then n is not divisible by 5. Prove that there is no integer solution to the equation 2x + 3y = 1 Prove that for any integer n, n^20 or 1 (remainder of 4) Prove by mathematical induction that: 1 + 3 + 5 + ... + (2n - 1) = n^2 Proofs by Discrete Structures (10 points each) Prove that for any sets A,B,C:A (BC)=(A B) (A C) Let g:N N be define by g(n)= n^2+n . Prove or disprove that g is injective Sequences (10 points) Find a closed formula for the sequence: 4, 9, 16, 25, 36, ... A computer virus doubles its spread every hour, but in addition, one new computer is infected manually at the start of each hour. If 1 computer is infected initially, how many are infected after 8 hours