小昭 ![](email.gif)
IP Address:
[ 14.0.155.158 ] |
回覆於: 2024/8/25 上午 11:45:00
1995=3*5*7*19 設n=abcddcba =(10^7+1)a+(10^6+10)b +(10^5+100)c+(10^4+10^3)d 當n=0 (mod 5)時,則a=5 當n=0 (mod 3)時,則 2(a+b+c+d)=0 (mod 3) a+b+c+d=0 (mod 3) b+c+d=1 (mod 3) ___ 當n=0 (mod 19)時,則 16a+2b+8c+18d=0 (mod 19) 8a+b+4c+9d=0 (mod 19) b+4c+9d=-2 (mod 19) ___ 當n=0 (mod 7)時,則 4a+4b+3d=0 (mod 7) 4b+3d=1 (mod 7) 4b+(7-4)d=1 (mod 7) 4b-4d=1 (mod 7) 4(b-d)=8 (mod 7) b-d=2 (mod 7) (b,d)=(2,0),(3,1),(4,2),(5,3),(6,4),(7,5), (8,6),(9,7),(0,5),(1,6),(2,7),(3,8),(4,9),(9,0) 共14種
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小昭 ![](email.gif)
IP Address:
[ 14.0.155.158 ] |
回覆於: 2024/8/25 下午 12:05:04
(b,d)=,c=,是否存在(b,c,d)使b+4c+9d=-2(mod19) (2,0),c=2,5,8, no (3,1),c=0,3,6,9,yes(3,6,1) (4,2),c=1,4,7, no (5,3),c=2,5,8, no (6,4),c=0,3,6,9,no (7,5),c=1,4,7, no (8,6),c=2,5,8, no (9,7),c=0,3,6,9,no (0,5),c=2,5,8, no (1,6),c=0,3,6,9,yes(1,0,6) (2,7),c=1,4,7, yes(2,7,7) (3,8),c=2,5,8, no (4,9),c=0,3,6,9,no (9,0),c=1,4,7, no 答案=53611635,51066015,52777725三種
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