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 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 September 2nd, 2017, 07:19 PM #1 Newbie   Joined: Sep 2017 From: NY Posts: 6 Thanks: 0 my problem Hey! (x+1)^(n+1)-(x-1)^(n+1)=y^n There is no solutions in total numbers x, y, n. n>1 How to show it?
 September 3rd, 2017, 05:22 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 895 "total numbers"? Do you mean "integers"?
 September 3rd, 2017, 05:38 AM #3 Newbie   Joined: Sep 2017 From: NY Posts: 6 Thanks: 0 Yes.
 October 17th, 2017, 07:47 AM #4 Member   Joined: May 2013 Posts: 34 Thanks: 1 look up Fermat's last theorem proof.
 October 17th, 2017, 09:05 AM #5 Senior Member   Joined: Sep 2016 From: USA Posts: 531 Thanks: 304 Math Focus: Dynamical systems, analytic function theory, numerics Try a simple example first. If $n=2$ then you want to prove that $(x+1)^3 - (x-1)^3 = y^2$ has no integral solutions. Suppose it did, then expanding gives us $6x^2 + 2 =y^2$. Do you see why this can't be true? Hint: compute this modulo 3. Now apply a similar idea to the general expression using the binomial theorem. Thanks from topsquark

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