Problem 3. Determine whether the statement is true or false. Prove the statement directly from definitions if it is true, and give a counterexample if it is false. (1) There exists an integer m 23 such that 6m² +27 is prime. (2) For all integers a and b, if a divides b, then a² divides b². (3) If m is an odd integer, then 3m² + 7m +12 is an even integer.