Assignment Use the Division Algorithm to establish the following: 1. The square of an integer is either of the form \( 3 k \) or \( 3 k+1 \) 2. The cube of an integer has one of the forms: \( 9 k, 9 k+1 \) or \( 9 k+8 \) 3. The fourth power of an integer is either of the form \( 5 \mathrm{kor} \) \( 5 k+1 \)
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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. 4. Prove that 3a^2 - 1 is never a perfect square. [Hint: Problem 3(a).]
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use division algorithm to show that the cube of any positive integer is of the form 9m,9m+1 or 9m+8?
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