一个有可能和哥德巴赫猜一样棒的数学规律（急待解决）用一个整数不断减去它反过来写的数,最终结果为零或不断循环,为什么?如：1 91-19=72 72-27=45 45-54=-9 -9-(-9)=02 123-321=-198 -198-(-891)=693 693-396

一个有可能和哥德巴赫猜一样棒的数学规律（急待解决）用一个整数不断减去它反过来写的数,最终结果为零或不断循环,为什么?如：1 91-19=72 72-27=45 45-54=-9 -9-(-9)=02 123-321=-198 -198-(-891)=693 693-396
一个有可能和哥德巴赫猜一样棒的数学规律（急待解决）
用一个整数不断减去它反过来写的数,最终结果为零或不断循环,为什么?
如：
1 91-19=72 72-27=45 45-54=-9 -9-(-9)=0
2 123-321=-198 -198-(-891)=693 693-396=297 297-792=-495
-495-(-594)=99 99-99=0
3 千位以上的数也一样,有的数会越减位数越小.
如：2746-6472=-3726 -3726-（-6273）=2547 2547-7452=-4905 -4905-（-5094）=189 然后再减为零.
但有的无限循环.
如：6534-4356=2178 2178-8712=-6534 -6534-（-4356）=-2178 -2178-（-8712）=6534 65934 659934也一样.
有的数也会变为多少个9的形式再变为零.
如：4995-5994=-999 -999-(-999)=0
我证了很久,但没搞定.如证2位数,10a+b-10b-a=9a-9b=9（a-b),但接下来就不好弄了.
有可能这个规律已被发现或证明,但无论怎样,我十分想得到答案,因为它困惑了我很久.

一个有可能和哥德巴赫猜一样棒的数学规律（急待解决）用一个整数不断减去它反过来写的数,最终结果为零或不断循环,为什么?如：1 91-19=72 72-27=45 45-54=-9 -9-(-9)=02 123-321=-198 -198-(-891)=693 693-396
10a+b-10b-a=9a-9b
其中9(a-b)=10(a-b)-(a-b)
设a>b,当然也可以b>a
则a-b肯定为一位数.
则10(a-b)必为十位上的数
所以
10(a-b)-(a-b)-10(a-b)+(a-b)=0

从21到9999，能循环的数有1012,1023,1034,1045,1067,1078,1089,1100,1122,1133,1144,1155,1177,1188,1199,1210,1232,1243,1254,1265,1287,1298,1320,1342,1353,1364,1375,1397,1408,1430,1452,1463,1474,1485,1507,1518,1540,...

全部展开

从21到9999，能循环的数有1012,1023,1034,1045,1067,1078,1089,1100,1122,1133,1144,1155,1177,1188,1199,1210,1232,1243,1254,1265,1287,1298,1320,1342,1353,1364,1375,1397,1408,1430,1452,1463,1474,1485,1507,1518,1540,1562,1573,1584,1595,1606,1617,1628,1650,1672,1683,1694,1705,1716,1727,1738,1760,1782,1793,1815,1826,1837,1848,1870,1892,1903,1925,1936,1947,1958,1980,2013,2024,2035,2046,2068,2079,2090,2101,2123,2134,2145,2156,2178,2189,2200,2211,2233,2244,2255,2266,2288,2299,2310,2321,2343,2354,2365,2376,2398,2409,2420,2431,2453,2464,2475,2486,2508,2519,2530,2541,2563,2574,2585,2596,2607,2618,2629,2640,2651,2673,2684,2695,2706,2717,2728,2739,2750,2761,2783,2794,2816,2827,2838,2849,2860,2871,2893,2904,2926,2937,2948,2959,2970,2981,3014,3025,3036,3047,3069,3091,3102,3124,3135,3146,3157,3179,3201,3212,3234,3245,3256,3267,3289,3300,3311,3322,3344,3355,3366,3377,3399,3410,3421,3432,3454,3465,3476,3487,3509,3520,3531,3542,3564,3575,3586,3597,3608,3619,3630,3641,3652,3674,3685,3696,3707,3718,3729,3740,3751,3762,3784,3795,3817,3828,3839,3850,3861,3872,3894,3905,3927,3938,3949,3960,3971,3982,4015,4026,4037,4048,4070,4092,4103,4125,4136,4147,4158,4180,4202,4213,4235,4246,4257,4268,4290,4301,4312,4323,4345,4356,4367,4378,4400,4411,4422,4433,4455,4466,4477,4488,4510,4521,4532,4543,4565,4576,4587,4598,4609,4620,4631,4642,4653,4675,4686,4697,4708,4719,4730,4741,4752,4763,4785,4796,4818,4829,4840,4851,4862,4873,4895,4906,4928,4939,4950,4961,4972,4983,5016,5027,5038,5049,5060,5071,5093,5104,5126,5137,5148,5159,5170,5181,5203,5214,5236,5247,5258,5269,5280,5291,5302,5313,5324,5346,5357,5368,5379,5390,5401,5412,5423,5434,5456,5467,5478,5489,5511,5522,5533,5544,5566,5577,5588,5599,5621,5632,5643,5654,5676,5687,5698,5709,5731,5742,5753,5764,5786,5797,5819,5841,5852,5863,5874,5896,5907,5929,5951,5962,5973,5984,6017,6028,6039,6050,6061,6072,6094,6105,6127,6138,6149,6160,6171,6182,6204,6215,6237,6248,6259,6270,6281,6292,6303,6314,6325,6347,6358,6369,6380,6391,6402,6413,6424,6435,6457,6468,6479,6490,6512,6523,6534,6545,6567,6578,6589,6600,6622,6633,6644,6655,6677,6688,6699,6710,6732,6743,6754,6765,6787,6798,6820,6842,6853,6864,6875,6897,6908,6930,6952,6963,6974,6985,7018,7029,7040,7051,7062,7073,7095,7106,7128,7139,7150,7161,7172,7183,7205,7216,7238,7249,7260,7271,7282,7293,7304,7315,7326,7348,7359,7370,7381,7392,7403,7414,7425,7436,7458,7469,7480,7491,7513,7524,7535,7546,7568,7579,7590,7601,7623,7634,7645,7656,7678,7689,7700,7711,7733,7744,7755,7766,7788,7799,7810,7821,7843,7854,7865,7876,7898,7909,7920,7931,7953,7964,7975,7986,8019,8041,8052,8063,8074,8096,8107,8129,8151,8162,8173,8184,8206,8217,8239,8261,8272,8283,8294,8305,8316,8327,8349,8371,8382,8393,8404,8415,8426,8437,8459,8481,8492,8514,8525,8536,8547,8569,8591,8602,8624,8635,8646,8657,8679,8701,8712,8734,8745,8756,8767,8789,8800,8811,8822,8844,8855,8866,8877,8899,8910,8921,8932,8954,8965,8976,8987,9020,9042,9053,9064,9075,9097,9108,9130,9152,9163,9174,9185,9207,9218,9240,9262,9273,9284,9295,9306,9317,9328,9350,9372,9383,9394,9405,9416,9427,9438,9460,9482,9493,9515,9526,9537,9548,9570,9592,9603,9625,9636,9647,9658,9680,9702,9713,9735,9746,9757,9768,9790,9801,9812,9823,9845,9856,9867,9878,9900,9911,9922,9933,9955,9966,9977,9988

收起

10(a-b)-(a-b)-10(a-b)+(a-b)=0

楼上两位虽然牛B，但还是没完全证明.