 An Equation Flying Past 3D Homer in Treehouse of Horror VI

1. Go to this text transcript of the 3-d Homer segment and Did You Notice? by James A. Cherry, and find the exact numbers in the equation shown above where numbers are raised to a power of 12. Verify that this matches what you see in the picture and write the equation here.

2. Is the right hand side of the equation even or odd? Why?

3. Is the left hand side of the equation even or odd? Why?

4. Use the answers to the last two questions to explain why this equation cannot hold.

5. What is the statement of Fermat's Last Theorem? If you don't know, look it up in your notes or on the web.

6. Use Fermat's Last Theorem (which Andrew Wiles proved was true) to explain why this equation cannot be true.

7. Yet, we do not need the full strength of Fermat's Last Theorem. Explain how we can show the equation is false if we know only that Fermat's Last Theorem doesn't hold when the power is 3 or 4. Then research the web in order to discuss who first proved Fermat's for these cases.

8. I decide to calculate the 12th root of 178212 + 184112. On my TI-83 Plus calculator. I type

1782^12 + 1841^12 ENTER

and obtain 2.541210259 E 39. I then take the 12th root by typing

^(1/12) ENTER

and obtain 1922. This really did happen on my calculator. Resolve the apparent conflict with questions 4 and 6. Homer emulating Thomas Edison in The Wizard of Evergreen Terrace

9. Go to this text transcript of The Wizard of Evergreen Terrace and find the equation where numbers are raised to a power of 12. Verify that this matches what you see in the picture and write the equation here.

10. Can an even/odd argument be used to justify that the 2nd equation is false? If so, then give the details, and if not, explain why.

11. Show two different mathematical reasons why the equation cannot hold. Hint: For one of the reasons, use the fact that 3 divides a number if and only if 3 divides the sum of the digits.

12. Which of the two sets of equations is closer to holding? Justify your answer.