I shall prove this by induction.
P(0): x^0 + y^0 = z^0. This is obvious. 1 + 1 does not equal 1.
P(k-1)=>P(k): Suppose x^k + y^k = z^k were to have solutions in x,
y, and z. Differentiate to obtain kx^(k-1) + ky^(k-1) = kz^(k-1) which
implies that x^(k-1) + y^(k-1) = z^(k-1). But by the inductive
hypothesis, this has no solutions in integers. Therefore, we apply the
Principle of Mathematical Induction, and we are done.
This theorem results in a number of interesting corollaries.
1. x^n + y^n = z^n has no solutions WHATSOEVER, integral, rational, or
real. Notice that the assumption that x, y, and z are integral is
2. Mathematicians have been deluding the general public for years about
the existence of Pythagorean triangles, such as the 3-4-5 right
triangle. Since the theorem actually covers all n greater than or equal
to 0, there are no solutions to the equation x^2 + y^2 = z^2 in
integers. Therefore, no Pythagorean triangles exist. I find it
truly hard to believe that this blinding of the public eye has been
allowed to continue for so long.
3. Furthermore, and this is the most amazing implication, NO TWO
NUMBERS CAN ADD TO ANY OTHER NUMBER! By the theorem, there are no
solutions to the equation x + y = z, where x, y, and z are any real
numbers. I find it truly fascinating that the human race has actually
allowed itself to believe that two numbers can add to another number,
when this statement is so plainly false. George Orwell was actually
quite prophetic when, in his "1984," he made the claim that 2+2 is not
4. But he was wrong to say that 2+2 is anything else, like 5 or 3;
indeed, this theorem shows that 2+2 cannot be anything at all.
I am trusting this information to you, my friends, because I honestly
believe that if word got out that all arithmetic were totally bogus,
the world would go crazy. For years, math teachers' paychecks have
relied on the (now disproved) maxim that 3+14 had an answer. If
principals were to throw them out in the street, as they certainly would
upon the common acceptance of this theorem, the mathematics teachers of
the world would rise up against the cruel, truth-preaching majority, and
the planet would collapse into dire civil war. Bombs would be
dropped. Judgment day would be at hand.
Please keep this dangerous information to yourselves; however, if
ever anyone asks you what 2+2 is, shout, "Absolutely nothing, dammit!"
and storm out of the room. It's the only right thing to do.
Continue the quest for knowledge!
>Hi all! I have discovered a truly remarkable proof of the assertion
>that x^n + y^n = z^n has no integer solutions when n > 2, first proposed
>by Fermat in the margin of one of his books and since studied and
>debated for centuries.
>I shall prove this by induction.
>This theorem results in a number of interesting corollaries.
>1. x^n + y^n = z^n has no solutions WHATSOEVER, integral, rational, or
>real. Notice that the assumption that x, y, and z are integral is
>3. Furthermore, and this is the most amazing implication, NO TWO
>NUMBERS CAN ADD TO ANY OTHER NUMBER! By the theorem, there are no
>solutions to the equation x + y = z, where x, y, and z are any real
>Continue the quest for knowledge!
Damn you, Josh! Ever since I read this on my computer, it refuses to
do any floating-point arithmetic. Pretty soon, this will extend to
integer processes as well and even my keyboard will stop wor