Pythagorean Theorem, Fermat's Last Theorem
Date: 5/16/96 at 11:52:4 From: Anonymous Subject: Geometry I have been challenged by a teacher to see if a cubed + b cubed = c cubed. We are doing the Pythagorean theorem. My question is, can the equation be done with 3 different numbers. It might be a trick question. Thanks.
Date: 7/12/96 at 12:8:59 From: Doctor Beth Subject: Re: Geometry Hi! If I understand correctly, you want to know if a^3 + b^3 = c^3 for 3 different positive integers (none of them 0). This is a famous theorem in mathematics, and it was proven about a year or so ago by Andrew Wiles that it cannot be done. Since you asked us this question, your teacher may have told you about Fermat's Last Theorem (which Fermat never proved) that a^n + b^n = c^n has no solutions of 3 distinct positive integers when n is also a positive integer that's larger than 2. Andrew Wiles' proof of this theorem uses some really advanced mathematics that even most professional mathematicians don't understand! If you wanted integers to solve a^3 + b^3 = c^3 and didn't require that they be positive, then you could let a = -1, b = 1 and c = 0. You also know that there are lots of numbers that solve the equation a^2 + b^2 = c^2, like a=3, b=4, and c=5, or also a = 5, b = 12, and c = 13. -Doctor Beth, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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