8. For any positive integer m, define: Sm :: the remainder when m2 1 is divided by 24. For example, for m : 6, we have 62 1 : 35, and the remainder when we divide 35 by 24 is 11. So Sf, : 11. (a) Build a table of values for Sm with 4 S m S 20. (You should find 510 : 3 and 515 : 8, for example.) It is fine to use a calculator, or even write a program, to do this. (b) A conjecture is a mathematical statement that lacks proof, but which is not known to be false. It is a fancy word for \"guess.\" While conjectures do not require proof, they must survive checking against all available data. Explain why the statement \"If m is odd, then Sm : O." is not a conjecture. (c) Make your own conjecture! Write a statement of the form \"if P, then Q,\" where P has some- thing to do with m and Q has something to do with 5,". (It is not so important that your conjecture turn out to be true, but it must agree with all the data from your table.)