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Almost universal ternary sums of pentagonal numbers

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 Added by Hai-Liang Wu
 Publication date 2020
  fields
and research's language is English




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For each integer $x$, the $x$-th generalized pentagonal number is denoted by $P_5(x)=(3x^2-x)/2$. Given odd positive integers $a,b,c$ and non-negative integers $r,s$, we employ the theory of ternary quadratic forms to determine when the sum $aP_5(x)+2^rbP_5(y)+2^scP_5(z)$ represents all but finitely many positive integers.



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78 - Rusen Li 2021
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197 - Simon Griffiths 2010
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