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a{n+1} = a{n}^3 + a{n}^2 and mod11

Source: 0

April 28, 2009
modular arithmeticgeometry3D geometry

Problem Statement

(a_n)_{n \equal{} 0}^\infty is a sequence on integers. For every n0 n \ge 0, a_{n \plus{} 1} \equal{} a_n^3 \plus{} a_n^2. The number of distinct residues of ai a_i in (mod11) \pmod {11} can be at most?
<spanclass=latexbold>(A)</span> 2<spanclass=latexbold>(B)</span> 3<spanclass=latexbold>(C)</span> 4<spanclass=latexbold>(D)</span> 5<spanclass=latexbold>(E)</span> 6<span class='latex-bold'>(A)</span>\ 2 \qquad<span class='latex-bold'>(B)</span>\ 3 \qquad<span class='latex-bold'>(C)</span>\ 4 \qquad<span class='latex-bold'>(D)</span>\ 5 \qquad<span class='latex-bold'>(E)</span>\ 6