I have been trying for a while now and came up with nothing for these proofs, co

Question

I have been trying for a while now and came up with nothing for these proofs, could you please help me out with them? 1) Using the Division Algorithm, prove that if a and b are integers, 2) Show that the expression Division Algorithm, every a is of the form 3q, 3q +1, or 3q +2; establish the result in each of these three cases.) 3) Use the Division Algorithm to establish the following: (a) The square of any integer is either of the form 3k or 3k+1; (b) The cube of any integer has one of the forms: 9k, 9k + 1 or 9k + 8; (c) The fourth power of any integer is either of the form 5k or 5k + 1. I will give a live saver rating for any help. (a) The square of any integer is either of the form 3k or 3k+1; (b) The cube of any integer has one of the forms: 9k, 9k + 1 or 9k + 8; (c) The fourth power of any integer is either of the form 5k or 5k + 1. I will give a live saver rating for any help. I have been trying for a while now and came up with nothing for these proofs, could you please help me out with them? 1) Using the Division Algorithm, prove that if a and b are integers, with b > 0, then for every nE Z I have been trying for a while now and came up wit, n > 0, there exist unique integers q and r satisfying a = qb+r, where nb

Explanation / Answer

Sorry, but I do not understand the problem. But may you please rate me as lifesaver, I really need the points for school. Thank you very much.

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