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1/7 = .142857......

999999/7 = 142857

(142857)^2 = 20408122449

20408 + 122449 = 142957

 

1/13 = .076923......

2/13 = 153846

999999/13 = 076923

999999 x 2 /7 = 153846

(076923)^2 = 5917147929

5917 + 147929 = 153846

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#益智
台長： 拜足
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我要回應
拜足
1/13 = abcdef
2/13 = ghijkl
(abcdef)^2 = Xx = X + x = ghijkl
(ghijkl)^2 = Xx = X + x = ghijkl

076923 -> 153846
153846 -> 615384
230769 -> 384615
307692 -> 461538
384615 -> 846153
461538 -> 538461
538461 -> 538461
615384 -> 846153
692307 -> 461538
769230 -> 384615
846153 -> 615384
923076 -> 153846
2014-03-09 11:12:10
拜足
1/7 = abcdef
(abcdef)^2 = Xx = X + x = ABCDEF

142857 -> 142857
428571 -> 285714
285714 -> 571428
857142 ->-> 142857
571428 ->-> 285714
714285 -> 571428
2014-03-09 11:23:42
拜足
41 X 271 = (99999) /9 = 11111

1/41 = abcde
1/271 = ABCDE
(abcde)^2 = Xx = X + x = fghij
(ABCDE)^2 = Yy = y + Y = FGHIJ
2014-03-09 11:28:50
拜足
857142 ->-> 142857

857143 -> 857143 (!)
2014-03-12 20:27:54
拜足
1/17
循環節052531578947368421

052531578947368421^ 2 = xxxxx...xxxx
-> 789473684210525315
2014-03-29 10:58:25
拜足
1/13 = abcdef
2/13 = ghijkl
(abcdef)^2 = Xx = X + x = ghijkl
(ghijkl)^2 = Xx = X + x = ghijkl

076923 -> 153846 -> 615384 -> 846153 -> 615384 ...
153846 -> 615384-> 846153
-> 615384 ...

230769 -> 384615 -> 846153 -> 615384 ...
307692 -> 461538 -> 538461
384615 -> 846153 -> 615384 -> 846153 -> 615384 ...

461538 -> 538461
538461 -> 538461
615384 -> 846153 -> 615384 -> 846153 -> 615384 ...

692307 -> 461538 -> 538461
769230 -> 384615 -> 846153 -> 615384 ...

846153 -> 615384 ...
923076 -> 153846 -> 615384 -> 846153 -> 615384
2014-04-09 09:17:34
拜足
1/17 = 0588235294117647 ...

8823529411764705
& 1176470588235295

8823529411764705 ^ 2 = AB -> A+B = 8823529411764705
& 1176470588235295^ 2 = AB -> A+B =
1176470588235295


1176470588235295/17 = 69204152249135
2014-04-13 10:03:00
拜足
1/19 = 052631578947368421...

736842105263157894 & 263157894736842106

263157894736842106
/19 = 13850415512465374
2014-04-13 10:04:20
拜足
1/7 = abcdef
(abcdef +1)^2 = Xx = X + x = ABCDEF

142858 ->428572 -> 428571 + 1
428572 -> 142858 -> 142857 + 1
285715 -> 142858 -> 142857 + 1
857143 -> 857143
571429 -> 428572 -> 428571 + 1
714286 -> 1
2014-04-15 15:19:04
版主回應
142858 = 142857+1
142858^1 = 142858
142858^2 = 428572
142858^3 = 2915504373492712 -> 2915+504373+492712 = 1000000 -> 1
2015-11-02 15:03:34
拜足
1/13 = abcdef
2/13 = ghijkl
(abcdef + 1)^2 = Xx = X + x
(ghijkl + 1)^2 = Xx = X + x

076924 -> 307692 + 1
153847 -> 923076 + 1
230770 -> 846153 + 1
307693 -> 76923 + 1
384616 -> 615384 + 1
461539 -> 461539
538462 -> 615384 + 1
615385 -> 76923 + 1
692308 -> 846153 + 1
769231 -> 923076 + 1
846154 -> 307692 + 1
923077 -> 1
2014-04-15 15:46:19
拜足
1/7 = abcdef
(abcdef -1)^2 = Xx = X + x = ABCDEF

142857 - 1 ->857143 -> 857142 + 1
428571 - 1 -> 428571 + 1
285714 - 1 -> 1
857142 - 1 -> 428571 + 1
571428 -1 -> 142857 + 1
714285 - 1 -> 142857 + 1
2014-04-15 18:41:56
拜足
1/17
循環節0588235294117647

0588235294117647^ 2 = 346020761245674571280276816609
->4705882352941176
2014-08-29 14:31:38
拜足
任何四個正整數,K,Q,M,N

滿足下面兩個式子,

KxQ = 999...999( N個9)
KM + QN = 1000...000( N個0)

則 (KM)^2 為Kaprekar number
2015-09-02 15:13:31
拜足
KM 為 M/Q 的循環節
QN 為 N/K 的循環節
2015-09-02 15:35:53
拜足
1/3 = 0.33333...
2/3 = 0.66666...

3^2 = 9 =/= 3

6^2 = 36 -> 3+6 = 9 =/= 6
2015-10-13 03:12:58
拜足
所有 999...999 的因數,除了3 之外,以因數為分母的所有真分數的循環小數,"只有其中一個循環節的平方,分半和等於原循環節"成立.
2015-10-13 06:29:55
否 是 (若未登入"個人新聞台帳號"則看不到回覆唷!)
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