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darijgr committed Sep 15, 2022
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4 changes: 2 additions & 2 deletions sols.tex
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\usepackage[type={CC}, modifier={zero}, version={1.0},]{doclicense}
%TCIDATA{OutputFilter=latex2.dll}
%TCIDATA{Version=5.50.0.2960}
%TCIDATA{LastRevised=Thursday, September 15, 2022 08:45:05}
%TCIDATA{LastRevised=Thursday, September 15, 2022 09:12:53}
%TCIDATA{SuppressPackageManagement}
%TCIDATA{<META NAME="GraphicsSave" CONTENT="32">}
%TCIDATA{<META NAME="SaveForMode" CONTENT="1">}
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\end{align*}
at which point it becomes clear that $b_{n}\in\mathbb{N}$ no longer holds for
all $n\in\mathbb{N}$. The same happens for all $r>2$ as long as $q=3$. (More
precisely, if we take $r>2$ and $q=3$, then the first $n$ that violates
precisely, if we take $r>2$ and $q=2$, then the first $n$ that violates
$b_{n}\in\mathbb{N}$ is $4$ or $5$ depending on whether $r$ is odd or even.
Proving this is a nice exercise!)

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