We introduce a polynomial E(d, t, x) in three variables that comes from the intersections of a family of ellipses described by Euler. For fixed odd integers \(t\ge 3\), the sequence of E(d, t, x) with d running through the integers produces, conjecturally, sequences of “twin composites” analogous to the twin primes of the integers. This polynomial and its lower degree relative R(d, t, x) have strikingly simple discriminants and resolvents. Moreover, the roots of R for certain values of d have continued fractions with at least two large partial quotients, the second of which mysteriously involves the 12th cyclotomic polynomial. Various related polynomials whose roots also have conjecturally strange continued fractions are also examined.

中文翻译：

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双复合材料，奇怪的连续分数和欧拉错过的变换（两次）

我们在三个变量中引入了多项式E（d，  t，  x），这些变量来自Euler描述的椭圆族的交集。对于固定的奇数整数\（t \ ge 3 \）来说，E（d，  t，  x）和d贯穿整数的序列，推测会产生类似于整数的双质数的“孪生复合”序列。该多项式及其较低阶的相对R（d，  t，  x）具有非常简单的判别式和分辨力。而且，R的根对于d的某些值，具有至少两个较大的商的连续分数，其中第二商神秘地涉及第12个环原子多项式。还检查了其根也具有推测上奇怪的连续分数的各种相关多项式。