////////////////////////////////////////////////////////////////
//
//     http://www.planetquantum.com/Solve/Level1/Den10/Page30.txt
//
////////////////////////////////////////////////////////////////

Generator:
S(12,5,10346)

Problem:
10349*x_1+10351*x_2+10352*x_3+10348*x_4+10347*x_5=10350 (mod 10346)
10353*x_1+10356*x_2+10355*x_3+10359*x_4+10357*x_5=10358 (mod 10354)
10362*x_1+10361*x_2+10364*x_3+10365*x_4+10360*x_5=10366 (mod 10363)
10368*x_1+10373*x_2+10370*x_3+10371*x_4+10369*x_5=10372 (mod 10367)
10380*x_1+10377*x_2+10374*x_3+10379*x_4+10376*x_5=10378 (mod 10375)
10386*x_1+10381*x_2+10385*x_3+10383*x_4+10387*x_5=10382 (mod 10384)
10390*x_1+10389*x_2+10392*x_3+10393*x_4+10394*x_5=10391 (mod 10388)
10399*x_1+10395*x_2+10397*x_3+10396*x_4+10398*x_5=10400 (mod 10401)
10406*x_1+10407*x_2+10408*x_3+10403*x_4+10404*x_5=10405 (mod 10402)
10409*x_1+10413*x_2+10414*x_3+10412*x_4+10415*x_5=10410 (mod 10411)
10416*x_1+10421*x_2+10420*x_3+10419*x_4+10418*x_5=10422 (mod 10417)
10429*x_1+10423*x_2+10426*x_3+10425*x_4+10424*x_5=10428 (mod 10427)

Solution:
x_1=2543766809115922620234239126087564172515
x_2=1547249793000371750428358217731602819720
x_3=2154145185944483083570515966928050477455
x_4=278771729945756634344419713367159473553
x_5=760286536215699911848417400092253109690