Euler's partition theorem and the combinatorics of -sequences
Euler's partition theorem and the combinatorics of -sequences
Euler's partition theorem and the combinatorics of -sequences
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Let u l <strong>and</strong> v l be <strong>the</strong> roots <strong>of</strong> <strong>the</strong> polynomial x 2 − lx + 1:<br />
Then<br />
u l = l + √ l 2 − 4<br />
; v l = l − √ l 2 − 4<br />
2<br />
2<br />
u l + v l = l; u l v l = 1.<br />
a (l)<br />
n = un l − v n l<br />
u l − v l<br />
.