Did I do something wrong?

Number Theory Level 3

I had been working on Fermat's Last Theorem and decided to try this equation:

$3987^{12} + 4365^{12}=n^{12}$ .

Using a calculator, I got the value of $n$ as $4472$ , which is impossible since Fermat's Last Theorem clearly states that $x^n + y^n = z^n$ is not possible for any positive integer value of $x, y$ and $z$ provided that $n > 2$ . What did I do wrong?

The calculator was wrong I did an error before the calculator I proved Fermat wrong I found an exception to the theorem

4 solutions

Vighnesh Raut
Apr 3, 2014

n is not exactly equal to 4472 , its real value = 4472.0000000070592907382135292414......

Jon Haussmann
Mar 27, 2014

The same problem was recently posted: https://brilliant.org/community-problem/my-calculator-says-its-true/?group=M7yny6PkVYl1&ref_id=123442

Sorry, didn't realise I had already answered it before but I forgot about it.

Sharky Kesa - 7 years, 2 months ago

Victor Paes Plinio
May 23, 2014

If you use a 8-digit calculator the real number $n=4472.0000000070592907382135292414494...$ (this number is irrational) appears as $4472$

Nishant Jain
Mar 27, 2014

There is a limit on any calculator's ALU capability. If the result goes beyond that max value, it can give any garbage value. In your case, since the no.s you have chosen are very large, calculator is likely to give you some shit..!!

Ha, it seemed most likely so that's what I did. I never new that calculators had crap limits like that.

Robert Fritz - 7 years, 2 months ago

Did I do something wrong?

4 solutions

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