do you know how to change modular equations into algebraic ones? if so, i suggest you do that. for instance, means for some .

after rewriting the statements that way, see if you can figure out what to do.

consider two cases: (1) x is even, (2) x is odd. show that the statement holds in either case. good ol' fashion algebra should do the trick. recall how to define even and odd integers.2.Prove that if a is an odd integer, then for any x in Z(set of integers), x^2 - x - a does not equal 0

do you know the method of mathematical induction? what have you tried?3. Use mathematical induction to prove that for any natural number n, 3 divides (2^(2n) - 1 ). Specify each step in the process clearly.

Thank you soo much (:

Let 3 divides for all

Clearly is true. (check this!)

Assume is true. Now we need to show that this implies is true.

Note that since is true, we have

for some .

So,