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Feb 26, 2013 at 22:23 comment added Gerry Myerson Perhaps a simpler proof: if $AP+BQ=1$, then $(x^2+1)A^*+2B^*=x^r$ for some polynomials $A^*$ and $B^*$ and some $r$, but at $x=1$ the left side is even, the right, odd.
Feb 26, 2013 at 21:46 history answered Wolfgang CC BY-SA 3.0