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Can we reduce Fermat last theorem problem to the case $z=x+1$ where $x^n + y^n = z^n$?

Why am I asking that? I found in that case and in case $n=3$ that difference of cubes: $1$,$7$,$19$,$37$ http://oeis.org/A003215

is a combination of diferrence of next sequence: http://oeis.org/A011934

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    Prior to Wiles's theorem that there is no integer solution, there was no such reduction, and Wiles's proof does not go through such a reduction.2012-04-08
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    I think we may be able to reduce to the cases $n=1$ or $n=2$. The condition specified adds nothing in either of these cases.2012-04-08
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    I don't get what you mean: *Centered hexagonal numbers are combinations of differences of $\sum (-1)^{n+1} n^3$?*2012-04-08
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    1-0=1,7-0=7,20-1=19,44-7=37,81-20=61,135-44=91 and so on....2012-04-08

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