Homer Simpson, in the 1998 episode “The Wizard of Evergreen Terrace,” claimed he had a counterexample to Fermat’s Last Theorem, and it was that 3987 12 + 4365 12 = 4472 12 . This exercise considers...

Homer Simpson, in the 1998 episode “The Wizard of Evergreen Terrace,” claimed he had a counterexample to Fermat’s Last Theorem, and it was that 3987¹²
+ 4365¹²
= 4472¹². This exercise considers whether it is possible to prove numerically that Homer is correct. Note that another (false) counterexample appeared in the 1995 episode “Treehouse of Horror VI.”

(a) Calculate 3987¹²
+ 4365¹²
− 4472¹². If Homer is right, what should the answer be?

(b) Calculate ( 3987¹²
+ 4365¹²)^1/12
− 4472. If Homer is right, what should the answer be?

(c) Calculate
If Homer is right, what should the answer be?

(d) CalculateIf Homer is right, what should the answer be?

(e) One argument that Homer could make is that (c) is the correct result and (a) and (b) can be ignored because if they are correct then you should not get a discrepancy between (a) and (d). Explain why MATLAB cannot be used to prove whether Homer is right or wrong.

Note: Homer’s blackboard containing the stated formula, along with a few other gems, can be found in Singh [2013]. It also explains why Homer appears to have an interest in mathematics and physics.