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April 26th, 2014, 10:08 AM   #1
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Bad "Proof" of Fermat's Last explained (in 3-5 minutes)

I had to comment on the error in a closed post.

The argument boiled down to:

$\displaystyle z = (C^n - B^n)/(A^{n-2})$

where z is an integer. The post claimed this is an immediate contradiction as the GCD of A, B, and C are 1. I can find many examples of (A, B, C, z) that work for n = 3.

Simply let A = C - B where gcd(B, C) = 1

Examples:
$\displaystyle 9^3 - 4^3$ is divisible by $\displaystyle 5^1$.
$\displaystyle 23^3 - 7^3$ is divisible by $\displaystyle 16^1$.

Suppose you want a counterexample for n > 3. If n = 11, we see that:

$\displaystyle (A = 2^9, B = 1001, C = 1001 + 2^9, z = (C^{11} - B^{11})/(2^9))$

is a perfectly good counterexample.

-- MMG

Last edited by mobilemathguy; April 26th, 2014 at 10:11 AM.
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