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Fermat simplified (Posted on 2011-06-21) Difficulty: 3 of 5
No positive integers fulfill the equation x^n+y^n=z^n if n>=z.

No Solution Yet Submitted by Ady TZIDON    
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Solution -- Spoiler | Comment 1 of 2

z>x and z>y. Say y>x.

Then y^n > x^n = z^n - y^n

= (z-y)( n terms in z and y)

> (z-y)(ny^n-1)

Cancel y^n-1

y > n(z-y) >= z(z-y) >= z(1) = z, an impossibility.

  Posted by xdog on 2011-06-21 14:39:20
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