0 3 0 4 4 4 3 1 3 1 x n k 0 1 5 6 n 2 4 4 4 2 2 n k x k 1 x n n k 0 k n xk 7 9 8 5 8 90 7 8 9 0 9 5 8 1 9 1 444 2 444 2 444 2 2 444 2 2 A 2 2 3 4 4 4 4 4 4 4 22 5 20 4 7 3 0 8 7 3 5 444 A 2 444 2 444 22 3 B n xk k n 1 x n k 0 n k k 0 1 x n n k Since n k n xk k k 0 x 1 x 14 2n 0 if k n n n k k 0 3 5 1 x n n n k 0 k n n k 0 k D n n k 0 k n n k 0 k 1 4 xk 5A 4 k 0 8C 1 1 1 x n 1 D xk 5A 4 0 1 1 k 8C n k even n k n n k k odd n 1 x n k 0 n xk k 4 6 5 k odd n 1 x k 0 n n 1 1 k k even 7 1 n n 2 n 1 E 4 n k 2 n 1 n xk k 21 1 1 F 4 1 E 1 F 4 n n n 2n 1 k k odd k n k even 6 1 6 1 1 8 1 1 1 4 4 1 7 1 8 1 1 1 1 1 4 1 4 1 6 1 8 6 A 8 4441 4 84 4 2 1 1 1 x k 0 1 n xk k 3 1 4 5 n 2 4 n 2 0 A 0 A 0 A 0 A 0G A G G G B 6 0 n n n n n 0 1 2 k n 0 A 0 A 0 A 0 A 0 A 0 A 0 A 0 A 0G A G G G 0G A G G G 2 0A 0 A 2 0 20 20 A E F 0 1 0 1 0 A 0 2 0 A 0 A 3 0 0 A 0G 0 G A G G 1 1 1 1 1 1 6 2 4 10 15 1 3 6 4 8 4 10 20 1 1 5 15 1 6 1 4F 1 3 1 9 8 1 1 2 2 3 3 J 2n 1 I 3 444H 5 1 3 5 E 2 3 H 1 1 1 1 2 2 1 3 3 3 1 J 8 1 J 3 G n n 1 1 k 0 k 1 1 2 1 2 1 4 1 3 3 1 8 1 4 6 4 1 16 1 5 10 10 5 1 32 1 6 15 20 15 6 1 64 1 1 1 1 2 1 1 1 4 1 10 15 1 6 10 6 1 3 4 5 1 1 3 1 1 20 1 15 6 1 4 5 10 6 1 3 1 1 1 A 2 2 1 5 1 3 1 6 15 n 4 1 10 5 20 i n 1 n n 1 1 2 2 n i i k i k 1 15 6 1 1 1 1 1 1 1 1 2 3 1 4 5 10 6 15 1 1 1 1 3 6 k i k 1 4 1 10 5 20 i n 15 n 1 1 k 1 1 1 1 6 6 3 4 5 10 A 1 A 3 6 15 A 1 A 2 1 A 1 4 1 10 5 20 1 15 6 1 1 0 1 1 1 1 1 1 1 6 2 3 1 4 5 10 15 1 1 1 1 3 6 1 1 4 1 10 5 20 15 1 1 1 6 1 1 1 0 1 1 2 2 1 4 3 2 3 4 2 6 5 2 10 6 2 15 20 1 9 4 1 10 5 15 16 1 6 25 1 36 0 1 1 1 1 1 1 1 1 0 1 1 2 2 1 4 3 2 3 4 2 6 5 2 10 6 2 15 1 4 1 10 5 20 9 15 16 1 6 1 36 1 1 K n2 i 0 1 0 1 2 1 2 3 2 3 1 0 2 1 3 2 n n 1 2 2 2 3 4 5 2 2 2 2 1 2 2 1 4 4 2 6 5 2 10 20 4 1 10 5 15 n 2 1 9 i n 1 2 n 1 n 1 2n 1 n 1 n 3 2 6 1 1 n n 1 n n i 1 1 3 2 3 6 2 15 I0 0 1 1 i 2 12 22 32 1 1 n 25 0 1 1 H 1 47 1 2 2 1 4 16 1 6 3 25 1 36 10 5 2 44444 44444 1 44444 1 44444 3 44444 1 4 1 5 1 1 2 15 1 3 6 10 6 2 1 1 1 4 6 15 20 1 5 10 n n 1 n 1 k k 1 k 44444 44444 1 44444 1 44444 3 44444 1 4 1 1 5 6 1 2 k even 1 3 6 10 15 2 1 1 20 1 5 10 15 n 2 n 1 k 1 1 4 6 44444 44444 1 44444 1 44444 3 44444 1 4 1 5 1 2 15 n k 0 1 3 6 10 6 2 1 1 15 2 1 5 10 20 n k 1 4 6 2n n 3 44444 44444 1 44444 1 44444 3 44444 1 4 3 0 1 n k n k A 0 1 1 if k 0 1 6 i 1 0 1 1 1 1 1 1 1 1 1 1 2 2 1 4 4 2 6 5 2 10 H 20 I0 2 6 10 15 1 3 1 1 4 20 1 5 10 6 15 Corollary k 1 n i i 1 H I0 H I0 n 1 n n 1 2 2 0 3 2 3 6 2 15 1 i n 1 k k 1 n 0 if k 0 or k n 5 2 1 1 9 4 1 10 5 15 16 1 6 25 1 36 n i 2 12 22 32 n2 i 0 1 0 1 2 1 2 3 2 3 1 0 2 1 3 2 n n 1 n n 1 n n i i 1 2 2 2 3 4 5 2 2 2 2 n 2 n 1 2 n 1 n 1 2n 1 n 1 n 3 2 6 4 8 1 8 2 L2N 0 6B 1 1 1 4 …
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