Created
November 27, 2018 15:40
-
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Save mewo2/41445bafeda857b24ffce3bf6485ba72 to your computer and use it in GitHub Desktop.
Program to find all x, y such that x * (x + y) is equal to the concatenation of the digits of x and y
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| 4 8 48 | |
| 34 68 3468 | |
| 12 96 1296 | |
| 334 668 334668 | |
| 112 896 112896 | |
| 38 988 38988 | |
| 3334 6668 33346668 | |
| 1112 8896 11128896 | |
| 910 9100 9109100 | |
| 304 9728 3049728 | |
| 102 9996 1029996 | |
| 33334 66668 3333466668 | |
| 11112 88896 1111288896 | |
| 2440 97600 244097600 | |
| 814 99308 81499308 | |
| 370 99900 37099900 | |
| 333334 666668 333334666668 | |
| 142858 857148 142858857148 | |
| 111112 888896 111112888896 | |
| 90910 909100 90910909100 | |
| 76924 923088 76924923088 | |
| 47620 952400 47620952400 | |
| 37038 962988 37038962988 | |
| 30304 969728 30304969728 | |
| 27028 973008 27028973008 | |
| 25642 974396 25642974396 | |
| 15874 984188 15874984188 | |
| 12988 987088 12988987088 | |
| 10990 989100 10990989100 | |
| 10102 989996 10102989996 | |
| 9010 991100 9010991100 | |
| 8548 991568 8548991568 | |
| 6994 993148 6994993148 | |
| 5292 994896 5292994896 | |
| 4330 995900 4330995900 | |
| 3862 996396 3862996396 | |
| 3664 996608 3664996608 | |
| 3368 996928 3368996928 | |
| 3004 997328 3004997328 | |
| 2850 997500 2850997500 | |
| 2458 997948 2458997948 | |
| 2332 998096 2332998096 | |
| 2080 998400 2080998400 | |
| 1444 999248 1444999248 | |
| 1288 999488 1288999488 | |
| 1222 999596 1222999596 | |
| 1002 999996 1002999996 | |
| 3333334 6666668 33333346666668 | |
| 1111112 8888896 11111128888896 | |
| 41842 9958396 418429958396 | |
| 13948 9986768 139489986768 | |
| 4650 9997500 46509997500 | |
| 33333334 66666668 3333333466666668 | |
| 11111112 88888896 1111111288888896 | |
| 9090910 90909100 909091090909100 | |
| 3030304 96969728 303030496969728 | |
| 1369864 98630208 136986498630208 | |
| 1010102 98989996 101010298989996 | |
| 990100 99010000 99010099010000 | |
| 729928 99270208 72992899270208 | |
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| 330034 99670268 33003499670268 | |
| 243310 99757100 24331099757100 | |
| 152208 99848448 15220899848448 | |
| 124534 99876268 12453499876268 | |
| 110012 99890896 11001299890896 | |
| 90010 99911100 9001099911100 | |
| 81104 99920128 8110499920128 | |
| 66358 99935148 6635899935148 | |
| 41512 99960896 4151299960896 | |
| 30004 99973328 3000499973328 | |
| 22120 99982400 2212099982400 | |
| 13838 99993388 1383899993388 | |
| 13564 99993808 1356499993808 | |
| 10002 99999996 1000299999996 | |
| 333333334 666666668 333333334666666668 | |
| 111111112 888888896 111111112888888896 | |
| 37037038 962962988 37037038962962988 | |
| 27027028 972973008 27027028972973008 | |
| 12345680 987654400 12345680987654400 | |
| 9009010 990991100 9009010990991100 | |
| 3003004 996997328 3003004996997328 | |
| 1001002 998999996 1001002998999996 | |
| 333668 999669328 333668999669328 | |
| 3333333334 6666666668 33333333346666666668 | |
| 1111111112 8888888896 11111111128888888896 | |
| 909090910 9090909100 9090909109090909100 | |
| 303030304 9696969728 3030303049696969728 | |
| 243902440 9756097600 2439024409756097600 | |
| 101010102 9898989996 1010101029898989996 | |
| 81300814 9918699308 813008149918699308 | |
| 36900370 9963099900 369003709963099900 | |
| 27100272 9972900096 271002729972900096 | |
| 22172950 9977827500 221729509977827500 | |
| 12300124 9987700688 123001249987700688 | |
| 7390984 9992610368 73909849992610368 | |
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| 3354580 9996648400 33545809996648400 | |
| 2463662 9997540396 24636629997540396 | |
| 1118194 9998890748 11181949998890748 | |
| 1099990 9998909100 10999909998909100 | |
| 900010 9999111100 9000109999111100 | |
| 372732 9999654096 3727329999654096 | |
| 366664 9999660608 3666649999660608 | |
| 300004 9999733328 3000049999733328 | |
| 122222 9999959596 1222229999959596 | |
| 100002 9999999996 1000029999999996 | |
| 33333333334 66666666668 3333333333466666666668 | |
| 11111111112 88888888896 1111111111288888888896 | |
| 4619152 99995402496 461915299995402496 | |
| 1539718 99998525228 153971899998525228 | |
| 513240 99999681600 51324099999681600 | |
| 333333333334 666666666668 333333333334666666666668 | |
| 142857142858 857142857148 142857142858857142857148 | |
| 111111111112 888888888896 111111111112888888888896 | |
| 90909090910 909090909100 90909090910909090909100 | |
| 76923076924 923076923088 76923076924923076923088 | |
| 47619047620 952380952400 47619047620952380952400 | |
| 37037037038 962962962988 37037037038962962962988 | |
| 30303030304 969696969728 30303030304969696969728 | |
| 27027027028 972972973008 27027027028972972973008 | |
| 25641025642 974358974396 25641025642974358974396 | |
| 15873015874 984126984188 15873015874984126984188 | |
| 12987012988 987012987088 12987012988987012987088 | |
| 10989010990 989010989100 10989010990989010989100 | |
| 10101010102 989898989996 10101010102989898989996 | |
| 9900990100 990099010000 9900990100990099010000 | |
| 9009009010 990990991100 9009009010990990991100 | |
| 8547008548 991452991568 8547008548991452991568 | |
| 6993006994 993006993148 6993006994993006993148 | |
| 5291005292 994708994896 5291005292994708994896 | |
| 4329004330 995670995900 4329004330995670995900 | |
| 3861003862 996138996396 3861003862996138996396 | |
| 3663003664 996336996608 3663003664996336996608 | |
| 3367003368 996632996928 3367003368996632996928 | |
| 3300330034 996699670268 3300330034996699670268 | |
| 3003003004 996996997328 3003003004996996997328 | |
| 2849002850 997150997500 2849002850997150997500 | |
| 2457002458 997542997948 2457002458997542997948 | |
| 2331002332 997668998096 2331002332997668998096 | |
| 2079002080 997920998400 2079002080997920998400 | |
| 1443001444 998556999248 1443001444998556999248 | |
| 1414427158 998585573548 1414427158998585573548 | |
| 1287001288 998712999488 1287001288998712999488 | |
| 1221001222 998778999596 1221001222998778999596 | |
| 1100110012 998899890896 1100110012998899890896 | |
| 1001001002 998998999996 1001001002998998999996 | |
| 999001000 999001000000 999001000999001000000 | |
| 900090010 999099911100 900090010999099911100 | |
| 819000820 999181000400 819000820999181000400 | |
| 777000778 999223000508 777000778999223000508 | |
| 761614624 999238386688 761614624999238386688 | |
| 693000694 999307000748 693000694999307000748 | |
| 481000482 999519001596 481000482999519001596 | |
| 471475720 999528526400 471475720999528526400 | |
| 429000430 999571001900 429000430999571001900 | |
| 407000408 999593002048 407000408999593002048 | |
| 366703338 999633299388 366703338999633299388 | |
| 351000352 999649002496 351000352999649002496 | |
| 333000334 999667002668 333000334999667002668 | |
| 300030004 999699973328 300030004999699973328 | |
| 297000298 999703003068 297000298999703003068 | |
| 273000274 999727003388 273000274999727003388 | |
| 267594328 999732409408 267594328999732409408 | |
| 259000260 999741003600 259000260999741003600 | |
| 253871542 999746132396 253871542999746132396 | |
| 231000232 999769004096 231000232999769004096 | |
| 189000190 999811005100 189000190999811005100 | |
| 157158574 999842847788 157158574999842847788 | |
| 143000144 999857006848 143000144999857006848 | |
| 128584288 999871423488 128584288999871423488 | |
| 117000118 999883008428 117000118999883008428 | |
| 111000112 999889008896 111000112999889008896 | |
| 108802090 999891207100 108802090999891207100 | |
| 100999900 999899010000 100999900999899010000 | |
| 100010002 999899999996 100010002999899999996 | |
| 99000100 999901010000 99000100999901010000 | |
| 91000092 999909010896 91000092999909010896 | |
| 89198110 999910813100 89198110999910813100 | |
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| 69237694 999930776748 69237694999930776748 | |
| 63000064 999937015808 63000064999937015808 | |
| 52386192 999947632896 52386192999947632896 | |
| 42861430 999957161900 42861430999957161900 | |
| 39000040 999961025600 39000040999961025600 | |
| 38227762 999961798396 38227762999961798396 | |
| 37000038 999963026988 37000038999963026988 | |
| 36267364 999963760208 36267364999963760208 | |
| 33666634 999966363068 33666634999966363068 | |
| 33336668 999966693328 33336668999966693328 | |
| 33000034 999967030268 33000034999967030268 | |
| 29732704 999970300928 29732704999970300928 | |
| 28207950 999971827500 28207950999971827500 | |
| 27000028 999973037008 27000028999973037008 | |
| 24326758 999975714348 24326758999975714348 | |
| 23079232 999976964096 23079232999976964096 | |
| 21000022 999979047596 21000022999979047596 | |
| 20584180 999979464400 20584180999979464400 | |
| 14428558 999985640748 14428558999985640748 | |
| 14287144 999985782848 14287144999985782848 | |
| 13000014 999987076908 13000014999987076908 | |
| 12742588 999987335888 12742588999987335888 | |
| 12089122 999987993596 12089122999987993596 | |
| 11222212 999988866896 11222212999988866896 | |
| 11000012 999989090896 11000012999989090896 | |
| 9910902 999990189996 9910902999990189996 | |
| 9891100 999990210000 9891100999990210000 | |
| 9181810 999990927100 9181810999990927100 | |
| 9000010 999991111100 9000010999991111100 | |
| 8108920 999992014400 8108920999992014400 | |
| 7769224 999992359488 7769224999992359488 | |
| 7693078 999992436908 7693078999992436908 | |
| 7000008 999993142848 7000008999993142848 | |
| 6861394 999993284348 6861394999993284348 | |
| 4809520 999995398400 4809520999995398400 | |
| 4762382 999995447596 4762382999995447596 | |
| 4247530 999995987900 4247530999995987900 | |
| 4029708 999996218448 4029708999996218448 | |
| 3740738 999996526588 3740738999996526588 | |
| 3475252 999996812496 3475252999996812496 | |
| 3297034 999997006268 3297034999997006268 | |
| 3060604 999997266128 3060604999997266128 | |
| 3000004 999997333328 3000004999997333328 | |
| 2940598 999997399468 2940598999997399468 | |
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| 2702974 999997666988 2702974999997666988 | |
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| 1020202 999999959996 1020202999999959996 | |
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| 3333333333334 6666666666668 33333333333346666666666668 | |
| 1111111111112 8888888888896 11111111111128888888888896 | |
| 188679245284 9811320754768 1886792452849811320754768 | |
| 126582278482 9873417721596 1265822784829873417721596 | |
| 62893081762 9937106918396 628930817629937106918396 | |
| 42194092828 9957805907408 421940928289957805907408 | |
| 20964360588 9979035639888 209643605889979035639888 | |
| 14064697610 9985935303100 140646976109985935303100 | |
| 2388344878 9997611659308 23883448789997611659308 | |
| 796114960 9999203897600 7961149609999203897600 | |
| 265371654 9999734666028 2653716549999734666028 | |
| 33333333333334 66666666666668 3333333333333466666666666668 | |
| 11111111111112 88888888888896 1111111111111288888888888896 | |
| 9090909090910 90909090909100 909090909091090909090909100 | |
| 3030303030304 96969696969728 303030303030496969696969728 | |
| 1010101010102 98989898989996 101010101010298989898989996 | |
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| 46490004650 99953509997500 4649000465099953509997500 | |
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| 21510002152 99978490002496 2151000215299978490002496 | |
| 12679092178 99987320915708 1267909217899987320915708 | |
| 7170000718 99992830013228 717000071899992830013228 | |
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| 1955454742 99998044596396 195545474299998044596396 | |
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| 109999990 99999890909100 10999999099999890909100 | |
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| 36666664 99999966060608 3666666499999966060608 | |
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| 12222222 99999995959596 1222222299999995959596 | |
| 10000002 99999999999996 1000000299999999999996 | |
| 333333333333334 666666666666668 333333333333334666666666666668 | |
| 111111111111112 888888888888896 111111111111112888888888888896 | |
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| 96871064614 999903128945708 96871064614999903128945708 | |
| 90000900010 999909999111100 90000900010999909999111100 | |
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| 73243975684 999926756037968 73243975684999926756037968 | |
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| 357457804 999999645339728 357457804999999645339728 | |
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| 3333333333333334 6666666666666668 33333333333333346666666666666668 | |
| 1111111111111112 8888888888888896 11111111111111128888888888888896 | |
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| 15220700152208 9984779299848448 152207001522089984779299848448 | |
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| 11001100110012 9988998899890896 110011001100129988998899890896 | |
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| 8058017727640 9991941982273600 80580177276409991941982273600 | |
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| 5941770647654 9994058229354028 59417706476549994058229354028 | |
| 5824111822948 9994175888178768 58241118229489994175888178768 | |
| 4293688278232 9995706311724096 42936882782329995706311724096 | |
| 4151100041512 9995848899960896 41511000415129995848899960896 | |
| 3000300030004 9996999699973328 30003000300049996999699973328 | |
| 2686005909214 9997313994094508 26860059092149997313994094508 | |
| 2211900022120 9997788099982400 22119000221209997788099982400 | |
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| prime_cache=[2,3,5,7,11,13,17,19] | |
| def primes(): | |
| """List all primes as a generator.""" | |
| for p in prime_cache: | |
| yield p | |
| p = prime_cache[-1] | |
| while True: | |
| p += 2 | |
| prime = False | |
| for q in prime_cache: | |
| if q*q > p: | |
| prime = True | |
| break | |
| elif p % q == 0: | |
| break | |
| if prime: | |
| prime_cache.append(p) | |
| yield p | |
| def factors(n): | |
| """Calculate the factors of n (as a set)""" | |
| if n == 1: | |
| return {1} | |
| lowestf = n | |
| for i in primes(): | |
| if i * i > n: | |
| break | |
| if n % i == 0: | |
| lowestf = i | |
| break | |
| newfs = factors(n // lowestf) | |
| facs = newfs | set(f * lowestf for f in newfs) | |
| return facs | |
| a = 1 | |
| while a < 1e18: # Change this to 1e19 to hang your computer until it figures out that 1,111,111,111,111,111,111 is prime | |
| a *= 10 | |
| for p in sorted(factors(a - 1)): | |
| if p * p > a: break | |
| q = (a - 1) // p | |
| x = q + 1 | |
| y = (p - 1) * x | |
| if y < a // 10: # Delete this test to allow solutions with leading zeroes | |
| continue | |
| print(x, y, x * (x + y)) |
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