Fermat’s

for

Yet in an episode of The Simpson’s it was noted that , apparently contradicting Fermat’s last theorem.

Of course this is not a contradiction because is not actually equal to .

So why did The Simpson’s episode say these two numbers were equal?

Well,

while

So, starting from the left we see that the digit in is a 9, while for it is an 8.

David Radcliffe (@daveinstpaul ) tweeted:

You can find thousands of near-misses by solving the following equation:

A^n+B^n = C^n + !

or A^n+B^n = C^n – !

The difference is always !. I tested these up to n = 1000 and these still hold.

Surely based on asymptotic argument, these are counter-examples to FLT?

38305^3 + 51762^3 = 57978^3

49193^3 + 50920^3 = 63086^3

I think I found a set of formulas which work to find the series of best “near solutions” to Fermat’s Last Theorem out to infinity. I can’t be sure … just have an ordinary PC and Lotus spreadsheet which is accurate

only to 18 digits. Anyone who would like to see the formulas can email me … I’ll attach my final spreadsheet, which does work for 55 equations in a row … I’m sure of that. HH