Playing with Fermat's Last Theorem
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Some results from playing with Fermat's Last Theorem | Some results from playing with Fermat's Last Theorem | ||
by Will Johnson, [mailto:wjhonson@aol.com wjhonson@aol.com] copyright 2001-4, all rights reserved. | by Will Johnson, [mailto:wjhonson@aol.com wjhonson@aol.com] copyright 2001-4, all rights reserved. | ||
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(Condition 1) x^n + y^n = z^n | (Condition 1) x^n + y^n = z^n | ||
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(Condition 4) gcd(x,y) = gcd(x,z) = gcd(y,z) = 1 that is, they share no common factors. | (Condition 4) gcd(x,y) = gcd(x,z) = gcd(y,z) = 1 that is, they share no common factors. | ||
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Theorem: Given the above conditions, show that z-x and z-y are each and independently, either nth powers or n times a nth power. | Theorem: Given the above conditions, show that z-x and z-y are each and independently, either nth powers or n times a nth power. | ||
