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 Posted: Tue 12:15, 29 Mar 2011 Post subject: A number theoretic function, the calculation of th |
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Seven times a number of functions the calculation of the mean
Non- negative integer k, with A (2) = VII. (G +21 k + l05k. +35 k. a 210k + l12) 2 Pu (7 ) to prove (1 ) When k = 1 , the left side ; Σa (m) a a (1), ¨ (Zl, on the right = 1 , on the holds. (2 ) Suppose k =,[link widoczny dla zalogowanych], l , there are ( 7) also established that the A7 (2) a , l. (, l +21 n '+105 n. +35 n a 21O, l +112) 2 ' (8 ) (3 ) When k =, l +1 , there A7 (2) = Σa (m) = Σ (17 (m) + thirty <2 + Im <2 a Σa (m) = A, (2) +2 nm <H. +1 Σa (m +2 Σ [a (m) +7 a (m) +21 a (m) +35 a (m) + state (235a (m) +21 a. (m) +7 a (m) +1 )]=== 2A, (2 ; A (2) A 2A (2) +7 A6 (2 l +2 in '+105 n. +35 n0-210n +112) 2 eleven +7 n (n +1) (, l '+14 n. +31 n a 46n +16) 2. +21 n. (ns +10 n +15, l -10 ) 2 one . +35 n (n +1) (, l0 +5 n - 2) 2 +7 N2 +2 n = (, l +1) ((, l +1) +21 (, l +1) ' Ten 105 (, l +1). +35 (+1). A 210 (, l +1 ) +112 ) 2 one. To sum up , ( 7) are true for any natural number . Then complete the proof of Lemma 2 . using Lemma 1 and Lemma 2, gives the proof of the theorem . A (N) = Σa () = Σa () + m <N, Il <Σa () + ... + Σa () +2 kl ≤ m <zh +2 N2- a l a , (N a 2-Σa () ; Σa '() + Σ (a ( Shí ) +1) + N A - Thirty <N thirty <21m <21J a 】 ... + Σ (a ( plus ) + (s-1)) a ΣA ()+<,, oj a 1J a 17ΣfA6 (2H1) +21 ΣA5 (2kH1) + oor a 1j a 135ΣfA4 (2k, +1) +35 Σi4A3 (2 ...) + Iof; o A 1l a 121ΣA2 (2 / +1) +7 ΣA (2 ...) + Σi2 (9) oioO will (1 ), ( 2), ( 3), ( 4 ), (5 ), (6 ) And ( 7) into (9 ), arranged, a 1A7 (N) = Σ [ Chi Chi 1 + 6 +1 (21 +14 i) + chi 1 ( 105 ten l0210i +84 i.) + chi i (35 + 630i +840 iz +280 i) Ten Chi 3 +1 (a 21O a 210i +1680 i +1680 i +560 i ') + Chi l (112-42O a 84O +840 i. +1680 i +672 i) + k +1 (224 for a 560i. +672 I +448 i) +128 i] 2 ~ + - then complete the proof .
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