Here are two conjectures: Conjecture 1: For all integers a,b and c, if a|b and a|c, then a|bc. Conjecture 2: For all integers a,b and c, if a|c and b|c, then ab|c. Decide whether each conjecture is true or false and prove/disprove your assertions.

In each of the following statements, n represents a positive integer. One of the statements is true and the other two are false.  If n is even, then n is not prime  if n is a square number, then n is not prime  if n is a prime number and n ≥ 10, then n+2 is prime or n+4 is prime.  A. What two statements are false and in each case give a counter example to show that it is false  B. Prove the true statement

Let a, b, and c be integers. Prove that if a divides b and a divides c,then a divides (b-c).

6. Prove that for all integers a, b, and c, if a? + b2 = c?, then at least one of a and b is even.