Lehmer ketma-ketligi - Lehmer sequence
Yilda matematika, a Lehmer ketma-ketligi a ning umumlashtirilishi Lukas ketma-ketligi.[1]
Algebraik munosabatlar
Agar a va b bo'lsa murakkab sonlar bilan
![{ displaystyle a + b = { sqrt {R}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/13ce25416f07bd0d5593163df101b31357ab5f7c)
![{ displaystyle ab = Q}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4e53151686169f596b930f8c5bc21d7a611ca6c9)
quyidagi shartlarda:
Keyinchalik, tegishli Lehmer raqamlari:
![{ displaystyle U_ {n} ({ sqrt {R}}, Q) = { frac {a ^ {n} -b ^ {n}} {a-b}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a7bb15ca31329fc1ffd792303c569852724f70b5)
uchun n g'alati va
![{ displaystyle U_ {n} ({ sqrt {R}}, Q) = { frac {a ^ {n} -b ^ {n}} {a ^ {2} -b ^ {2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7ae7a894f3ec001671f2d40c130b46680771f236)
uchun n hatto.
Ularning sherik raqamlari:
![{ displaystyle V_ {n} ({ sqrt {R}}, Q) = { frac {a ^ {n} + b ^ {n}} {a + b}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/63a64fad5157cf84ad69ce7ef4ebf5b5b65444c4)
uchun n toq va
![{ displaystyle V_ {n} ({ sqrt {R}}, Q) = a ^ {n} + b ^ {n}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c09c797de23a710a9da071a907f57e45b8182e89)
uchun n hatto.
Takrorlash
Lehmer raqamlari chiziqli hosil qiladi takrorlanish munosabati bilan
![{ displaystyle U_ {n} = (R-2Q) U_ {n-2} -Q ^ {2} U_ {n-4} = (a ^ {2} + b ^ {2}) U_ {n-2 } -a ^ {2} b ^ {2} U_ {n-4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/52418adc0c0fbcdce4d7f9e1186ed50a50d2e97f)
boshlang'ich qiymatlari bilan
. Xuddi shunday sheriklar ketma-ketligini ham qondiradi
![{ displaystyle V_ {n} = (R-2Q) V_ {n-2} -Q ^ {2} V_ {n-4} = (a ^ {2} + b ^ {2}) V_ {n-2 } -a ^ {2} b ^ {2} V_ {n-4}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e7c5da39a306123b42dae553ff5db47ec194a89f)
boshlang'ich qiymatlari bilan ![{ displaystyle V_ {0} = 2, V_ {1} = 1, V_ {2} = R-2Q = a ^ {2} + b ^ {2}, V_ {3} = R-3Q = a ^ { 2} -ab + b ^ {2}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f16294606156d8e50fa1aaef5d306c756fb46f4a)
Malumot
- ^ Vayshteyn, Erik V. "Lehmer raqami". mathworld.wolfram.com. Olingan 2020-08-11.