Number Theory
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Somos Polynomials
Somos Polynomials Define a sequence with: S(1) = x , S(2) = S(3) = 1 , S(4) = y , S(n) = x*y*z*(S(n-1)*S(n-3)+S(n-2)^2)/S(n-4) if n 4 . The first observation is that this definition does produce polynomials with positive integer coefficients in the three indeterminates x , y , z. The proof is by induction. Another observation is that S(n) can be easily extended to n 1 so that it still ...
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Numerical Analysis@