daf3 - 3 libxz `'ryz ,zihxwqic dwihnznl `ean `'ryz ledipe...

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`''ryz ,zihxwqic dwihnznl `ean 3 libxz `''ryz ledipe diiyrz zqcpdl zihxwqic dwihnznl `ean - 3 sc . N * = { 1 , 2 , 3 , . . . } , N = { 0 , 1 , 2 , 3 , . . . } :mipeniq :egiked .1 . 1 2 + 2 2 + 3 2 + . . . + n 2 = n ( n +1)(2 n +1) 6 , n 1 lkl .` . 30 -a wlgzn n 5 - n ,irah n lkl .a . 8 -a wlgzn 5 n +1 + 2 · 3 n + 1 ,irah n lkl .b , n 2 xear a n = a n - 1 + a n - 2 -e , a 1 = 1 , a 0 = 1 :i''r zxcbend i'v`peait zxcqy divwecpi`a egiked .2 :zniiwn a n = 1 5 h‡ 1 + 5 2 · n +1 - 1 - 5 2 · n +1 i .miipey`x mixtqn ly dltknk daizkl ozip , n > 1 irah xtqn lk ik egiked .3 . k, t N xy`k , n = 3 k + 5 t -k dbvdl ozip n 8 irah xtqn lk ik egiked .4 . 5 -a `le , 3 -a `l , 2 -a `l ,miwlgzn mpi` 3000 -e 1 oia mixtqn dnk .` .5 . 8 -a `le , 6 -a `l , 5 -a `l ,miwlgzn mpi` 3000 -e 1 oia mixtqn dnk .a , run , fast mitvxdn cg` s` zellek `ly { a, b, c, . . . , x, y, z } zeize`d 26 ly zexenzd xtqn z` e`vn .6 . dog :( a n xear zyxetn dxev e`vn) ze`ad dbiqpd ze`eeyn z` exzit .7 . a 1 = 3 , a 0 = 2
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daf3 - 3 libxz `'ryz ,zihxwqic dwihnznl `ean `'ryz ledipe...

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