# Linear Congruences

## Submit

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## Problem

Solve systems of linear congruences (modular equations).
Note: Not all are solvable using the Chinese Remainder Theorem, and some aren't solvable at all!

http://mathworld.wolfram.com/LinearCongruenceEquation.html
http://en.wikipedia.org/wiki/Chinese_Remainder_Theorem
http://en.wikipedia.org/wiki/Method_of_successive_substitution

## Options

exec is denied

now post-mortem time, all source codes will be revealed

## Sample input:_

```x = 3 (mod 4)

x = 4 (mod 3)

x = 1 (mod 2)
x = 2 (mod 3)
x = 3 (mod 4)
x = 4 (mod 5)
x = 5 (mod 6)
x = 0 (mod 7)

x = 2 (mod 3)
x = 3 (mod 5)
x = 2 (mod 7)

```

## Sample output:

```3 + 4k
no solutions
119 + 420k
23 + 105k
```

## Sample input:_

```x = 0 (mod 3)
x = 2 (mod 10)

x = 0 (mod 5)
x = 3 (mod 10)

x = 0 (mod 7)
x = 5 (mod 10)

x = 0 (mod 11)
x = 7 (mod 10)

x = 0 (mod 13)
x = 11 (mod 100)

x = 0 (mod 17)
x = 13 (mod 100)

x = 0 (mod 19)
x = 17 (mod 100)

x = 0 (mod 23)
x = 19 (mod 100)

x = 0 (mod 29)
x = 23 (mod 100)

x = 0 (mod 31)
x = 29 (mod 100)

x = 0 (mod 37)
x = 31 (mod 100)

x = 0 (mod 41)
x = 37 (mod 100)

x = 0 (mod 43)
x = 41 (mod 100)

x = 0 (mod 47)
x = 43 (mod 100)

x = 0 (mod 53)
x = 47 (mod 100)

x = 0 (mod 59)
x = 53 (mod 100)

x = 0 (mod 61)
x = 59 (mod 100)

x = 0 (mod 67)
x = 61 (mod 100)

x = 0 (mod 71)
x = 67 (mod 100)

x = 0 (mod 73)
x = 71 (mod 100)

x = 0 (mod 79)
x = 73 (mod 100)

x = 0 (mod 83)
x = 79 (mod 100)

x = 0 (mod 89)
x = 83 (mod 100)

x = 0 (mod 97)
x = 89 (mod 100)

```

## Sample output:

```12 + 30k
no solutions
35 + 70k
77 + 110k
611 + 1300k
1513 + 1700k
817 + 1900k
1219 + 2300k
2523 + 2900k
1829 + 3100k
2331 + 3700k
2337 + 4100k
3741 + 4300k
3243 + 4700k
5247 + 5300k
3953 + 5900k
1159 + 6100k
5561 + 6700k
5467 + 7100k
1971 + 7300k
6873 + 7900k
1079 + 8300k
4183 + 8900k
3589 + 9700k
```

## Sample input:_

```x = 3 (mod 5)
x = 5 (mod 8)

x = 5 (mod 8)
x = 3 (mod 4)

x = 3 (mod 4)
x = 2 (mod 7)
x = 1 (mod 9)

x = 0 (mod 2)
x = 0 (mod 3)
x = 0 (mod 5)
x = 0 (mod 7)
x = 0 (mod 11)

x = 1 (mod 2)
x = 1 (mod 3)
x = 1 (mod 5)
x = 1 (mod 7)
x = 1 (mod 11)

x = 1 (mod 2)
x = 2 (mod 3)
x = 3 (mod 5)
x = 4 (mod 7)
x = 5 (mod 11)

x = 1 (mod 2)
x = 2 (mod 3)
x = 4 (mod 5)
x = 6 (mod 7)
x = 10 (mod 11)

x = 2 (mod 2)
x = 4 (mod 3)
x = 6 (mod 5)
x = 8 (mod 7)
x = 10 (mod 11)

x = 34 (mod 49)
x = 9 (mod 90)
x = 9 (mod 90)
x = 66 (mod 71)
x = 0 (mod 3)

x = 44 (mod 85)
x = 76 (mod 81)
x = 4 (mod 16)
x = 38 (mod 98)
x = 4 (mod 16)
x = 59 (mod 95)
x = 31 (mod 33)

x = 35 (mod 87)
x = 31 (mod 32)
x = 31 (mod 88)
x = 11 (mod 93)
x = 8 (mod 15)
x = 5 (mod 6)
x = 6 (mod 29)
x = 40 (mod 49)
x = 35 (mod 87)

x = 34 (mod 63)
x = 7 (mod 9)
x = 9 (mod 34)
x = 13 (mod 42)
x = 13 (mod 28)
x = 49 (mod 100)

x = 10 (mod 27)
x = 37 (mod 96)
x = 16 (mod 59)

x = 7 (mod 49)
x = 1 (mod 31)
x = 17 (mod 24)
x = 24 (mod 43)
x = 24 (mod 43)

x = 1 (mod 4)
x = 1 (mod 44)
x = 5 (mod 36)
x = 5 (mod 68)
x = 5 (mod 9)

x = 10 (mod 15)
x = 76 (mod 78)
x = 4 (mod 24)
x = 14 (mod 49)
x = 0 (mod 10)
x = 68 (mod 79)
x = 42 (mod 94)
x = 14 (mod 49)

x = 36 (mod 45)
x = 53 (mod 61)
x = 6 (mod 7)
x = 6 (mod 60)
x = 14 (mod 64)
x = 54 (mod 72)
x = 9 (mod 31)

x = 20 (mod 94)
x = 4 (mod 54)
x = 20 (mod 47)
x = 20 (mod 94)

x = 9 (mod 10)
x = 1 (mod 3)
x = 13 (mod 39)
x = 19 (mod 31)
x = 29 (mod 40)
x = 3 (mod 86)
x = 53 (mod 64)
x = 3 (mod 86)

x = 76 (mod 86)
x = 20 (mod 27)
x = 16 (mod 49)
x = 10 (mod 16)
x = 71 (mod 87)
x = 2 (mod 84)

x = 37 (mod 43)
x = 80 (mod 86)
x = 4 (mod 8)
x = 15 (mod 79)
x = 72 (mod 90)
x = 15 (mod 79)

x = 5 (mod 32)
x = 5 (mod 54)
x = 5 (mod 18)

x = 9 (mod 41)
x = 43 (mod 88)
x = 89 (mod 94)
x = 43 (mod 88)
x = 43 (mod 44)
x = 27 (mod 36)
x = 33 (mod 34)

x = 49 (mod 94)

x = 1 (mod 2)
x = 75 (mod 90)
x = 48 (mod 53)
x = 3 (mod 87)
x = 19 (mod 22)
x = 19 (mod 23)

x = 13 (mod 40)
x = 13 (mod 15)
x = 43 (mod 69)
x = 13 (mod 36)

x = 10 (mod 63)
x = 10 (mod 63)
x = 2 (mod 29)
x = 30 (mod 61)
x = 3 (mod 49)
x = 50 (mod 59)
x = 10 (mod 70)

x = 75 (mod 93)
x = 24 (mod 26)
x = 12 (mod 21)
x = 6 (mod 60)
x = 12 (mod 42)
x = 33 (mod 63)
x = 62 (mod 83)

x = 18 (mod 55)
x = 1 (mod 39)
x = 37 (mod 41)
x = 28 (mod 29)
x = 5 (mod 19)
x = 18 (mod 44)

x = 19 (mod 63)
x = 10 (mod 36)
x = 19 (mod 27)
x = 33 (mod 79)

x = 8 (mod 12)
x = 26 (mod 30)
x = 0 (mod 2)
x = 18 (mod 79)
x = 54 (mod 61)
x = 34 (mod 71)
x = 8 (mod 28)
x = 41 (mod 45)

x = 1 (mod 3)
x = 34 (mod 63)
x = 22 (mod 66)
x = 90 (mod 98)
x = 6 (mod 35)
x = 13 (mod 21)

x = 49 (mod 56)
x = 65 (mod 82)
x = 25 (mod 87)
x = 7 (mod 21)
x = 1 (mod 45)
x = 1 (mod 2)

x = 24 (mod 25)
x = 0 (mod 14)
x = 34 (mod 38)
x = 0 (mod 28)
x = 4 (mod 5)
x = 4 (mod 10)

x = 10 (mod 30)
x = 4 (mod 18)
x = 0 (mod 35)
x = 0 (mod 7)
x = 25 (mod 31)

x = 12 (mod 21)
x = 0 (mod 6)
x = 12 (mod 35)
x = 12 (mod 38)
x = 12 (mod 31)
x = 12 (mod 14)

x = 3 (mod 4)
x = 15 (mod 29)
x = 1 (mod 2)
x = 3 (mod 6)
x = 22 (mod 31)

x = 16 (mod 40)
x = 0 (mod 8)
x = 21 (mod 35)

```

## Sample output:

```13 + 40k
no solutions
163 + 252k
0 + 2310k
1 + 2310k
1523 + 2310k
2309 + 2310k
no solutions
279 + 313110k
724 + 1128148560k
383 + 232589280k
349 + 107100k
901 + 50976k
497 + 1567608k
617 + 6732k
700 + 283821720k
846 + 38122560k
490 + 2538k
949 + 16635840k
506 + 26396496k
252 + 1222920k
5 + 864k
747 + 25945128k
49 + 94k
525 + 34997490k
733 + 8280k
640 + 460276110k
726 + 42145740k
898 + 193830780k
586 + 59724k
176 + 431107740k
286 + 48510k
721 + 2996280k
224 + 13300k
490 + 19530k
12 + 123690k
363 + 10788k
56 + 280k
```

## Ranking

### Ruby_

RankUserSizeTimeDateStatistics
1kaki2530.22372009/06/24 16:27:060B / 114B / 131B
2kaki2460.48092009/07/10 01:55:430B / 106B / 133B

### Perl_

RankUserSizeTimeDateStatistics
1tybalt891030.52132009/06/24 17:36:520B / ?B / ?B
2mitch schwartz1000.14932013/01/03 01:59:200B / ?B / ?B
3mitchs (tybalt89) (namefix)1000.07422014/02/14 12:27:580B / 32B / 62B

### Python_

RankUserSizeTimeDateStatistics
1hallvabo2261.28802009/06/24 08:21:270B / 120B / 76B
2lifthrasiir2270.26282009/06/12 23:39:420B / 118B / 88B
3tryeng2410.92842009/05/28 01:22:500B / 131B / 70B

### Common LISP_

RankUserSizeTimeDateStatistics
1kozima2541.44532009/06/24 13:30:400B / 149B / 82B
2kozima2521.60782009/06/25 09:05:510B / 148B / 82B

### JavaScript_

RankUserSizeTimeDateStatistics
1nn2310.48682009/05/30 17:43:380B / 106B / 120B
2murky-satyr2130.13362009/11/29 22:30:530B / 100B / 108B

### J_

RankUserSizeTimeDateStatistics
1I., S.1140.13502012/08/06 20:59:380B / 28B / 81B

### C_

RankUserSizeTimeDateStatistics
151b1890.06732009/06/22 00:16:050B / 98B / 87B
2ozy4dm1900.14422009/06/17 14:18:150B / 94B / 92B
3funnything1970.02952009/06/21 07:46:080B / 93B / 99B
4pi80273420.04042009/05/29 10:14:280B / 186B / 136B
551b1790.02292009/06/27 21:49:220B / 88B / 87B

### D_

RankUserSizeTimeDateStatistics
151b2160.04712009/06/28 21:23:170B / 110B / 96B

RankUserSizeTimeDateStatistics
1notogawa1800.16822009/06/11 23:34:080B / ?B / ?B
2moriA1880.19842009/06/19 00:26:010B / 100B / 71B

### AWK_

RankUserSizeTimeDateStatistics
1nn1760.19142009/05/30 20:15:050B / 78B / 90B

### Postscript_

RankUserSizeTimeDateStatistics
1yshl(bin)1971.42692009/06/06 20:24:0382B / 68B / 43B
2yshl3351.47702009/06/06 20:23:360B / 239B / 47B

### Groovy_

RankUserSizeTimeDateStatistics
1murky-satyr2493.84562009/11/29 22:17:470B / 119B / 120B
2nn2748.22932009/11/07 00:33:560B / 142B / 120B

### Language Ranking_

RankLangUserSizeScore
1Perlmitchs (tybalt89) (namefix)10010000
2JI., S.1148771
3AWKnn1765681
4C51b1795586