Question: This is my math homework, do question 16, thanks. that any Integer of the ToTHI S4 + 2 I not a perfect square. (b) Prove

This is my math homework, do question 16, thanks.

that any Integer of the ToTHI S4 + 2 I not a perfect square. (b) Prove that any integer of the form 4k + 2 or 4k + 3 is not a perfect square. (c) Prove that any integer of the form 5k + 2 or 5k + 3 is not a perfect square. (d) Prove that any integer of the form 6k + 2 or 6k + 5 is not a perfect square. #16. (a) Prove that any integer of the form 7k + 3, 7k + 5, or 7k + 6 is not a perfect square. (b) Prove that any integer of the form 8k + r, where r = 2, 3, 5, 6 or 7 is not a perfect square. (c) Using information from this problem and the previous problem only, what integers from 1 to 100 inclusive are possibly perfect squares? That is, possibly the square of an integer? Hint: By part (a) of the previous problem, we have ruled out the integers: 2, 5, 8, 11, 14, 17, 20, 23, ..., 98 as perfect squares. D

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