Prove that every odd integer is a difference of two squares. For example, 7 42 - 32. Give a direct proof. [Hint: You might find it helpful to first write a few odd numbers in this way to figure out a pattern that will aid you in the proof.] (9 Pts.)

Q: Let T = {o E S4|0(3) = 3}. (a) Show that T is a subgroup of S4. (b) Prove that T= S3.

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Q: +y-9y-0 (0)-1

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Q: Exercises: Classify the follauing e quations. ( 0DE, PDE, order, linearity) ') yol + 2e*y" +yy'= t",...

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Q: 01. Determine the splitting field of x4 + x2 + 1 over Q. Also find its degree over Q.

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A: W and Y do not represent tariff revenue. They are deadweight loss.