28-Jul-2021 00:29:07 diophantine_3d_test(): MATLAB/Octave version 9.9.0.1467703 (R2020b) Test diophantine_3d(). diophantine_3d_nonnegative_test diophantine_3d_nonnegative returns the nonnegative solutions of a Diophantine equation in three variables. 6*x1+15*x2+10*x3 = 60 6 solutions found. 1: 6*0+15*4+10*0 = 60 2: 6*5+15*2+10*0 = 60 3: 6*10+15*0+10*0 = 60 4: 6*0+15*2+10*3 = 60 5: 6*5+15*0+10*3 = 60 6: 6*0+15*0+10*6 = 60 5*x1+3*x2+7*x3 = 24 5 solutions found. 1: 5*0+3*8+7*0 = 24 2: 5*3+3*3+7*0 = 24 3: 5*1+3*4+7*1 = 24 4: 5*2+3*0+7*2 = 24 5: 5*0+3*1+7*3 = 24 2*x1+4*x2+5*x3 = 80 97 solutions found. 1: 2*40+4*0+5*0 = 80 2: 2*38+4*1+5*0 = 80 3: 2*36+4*2+5*0 = 80 4: 2*34+4*3+5*0 = 80 5: 2*32+4*4+5*0 = 80 6: 2*30+4*5+5*0 = 80 7: 2*28+4*6+5*0 = 80 8: 2*26+4*7+5*0 = 80 9: 2*24+4*8+5*0 = 80 10: 2*22+4*9+5*0 = 80 11: 2*20+4*10+5*0 = 80 12: 2*18+4*11+5*0 = 80 13: 2*16+4*12+5*0 = 80 14: 2*14+4*13+5*0 = 80 15: 2*12+4*14+5*0 = 80 16: 2*10+4*15+5*0 = 80 17: 2*8+4*16+5*0 = 80 18: 2*6+4*17+5*0 = 80 19: 2*4+4*18+5*0 = 80 20: 2*2+4*19+5*0 = 80 21: 2*0+4*20+5*0 = 80 22: 2*35+4*0+5*2 = 80 23: 2*33+4*1+5*2 = 80 24: 2*31+4*2+5*2 = 80 25: 2*29+4*3+5*2 = 80 26: 2*27+4*4+5*2 = 80 27: 2*25+4*5+5*2 = 80 28: 2*23+4*6+5*2 = 80 29: 2*21+4*7+5*2 = 80 30: 2*19+4*8+5*2 = 80 31: 2*17+4*9+5*2 = 80 32: 2*15+4*10+5*2 = 80 33: 2*13+4*11+5*2 = 80 34: 2*11+4*12+5*2 = 80 35: 2*9+4*13+5*2 = 80 36: 2*7+4*14+5*2 = 80 37: 2*5+4*15+5*2 = 80 38: 2*3+4*16+5*2 = 80 39: 2*1+4*17+5*2 = 80 40: 2*30+4*0+5*4 = 80 41: 2*28+4*1+5*4 = 80 42: 2*26+4*2+5*4 = 80 43: 2*24+4*3+5*4 = 80 44: 2*22+4*4+5*4 = 80 45: 2*20+4*5+5*4 = 80 46: 2*18+4*6+5*4 = 80 47: 2*16+4*7+5*4 = 80 48: 2*14+4*8+5*4 = 80 49: 2*12+4*9+5*4 = 80 50: 2*10+4*10+5*4 = 80 51: 2*8+4*11+5*4 = 80 52: 2*6+4*12+5*4 = 80 53: 2*4+4*13+5*4 = 80 54: 2*2+4*14+5*4 = 80 55: 2*0+4*15+5*4 = 80 56: 2*25+4*0+5*6 = 80 57: 2*23+4*1+5*6 = 80 58: 2*21+4*2+5*6 = 80 59: 2*19+4*3+5*6 = 80 60: 2*17+4*4+5*6 = 80 61: 2*15+4*5+5*6 = 80 62: 2*13+4*6+5*6 = 80 63: 2*11+4*7+5*6 = 80 64: 2*9+4*8+5*6 = 80 65: 2*7+4*9+5*6 = 80 66: 2*5+4*10+5*6 = 80 67: 2*3+4*11+5*6 = 80 68: 2*1+4*12+5*6 = 80 69: 2*20+4*0+5*8 = 80 70: 2*18+4*1+5*8 = 80 71: 2*16+4*2+5*8 = 80 72: 2*14+4*3+5*8 = 80 73: 2*12+4*4+5*8 = 80 74: 2*10+4*5+5*8 = 80 75: 2*8+4*6+5*8 = 80 76: 2*6+4*7+5*8 = 80 77: 2*4+4*8+5*8 = 80 78: 2*2+4*9+5*8 = 80 79: 2*0+4*10+5*8 = 80 80: 2*15+4*0+5*10 = 80 81: 2*13+4*1+5*10 = 80 82: 2*11+4*2+5*10 = 80 83: 2*9+4*3+5*10 = 80 84: 2*7+4*4+5*10 = 80 85: 2*5+4*5+5*10 = 80 86: 2*3+4*6+5*10 = 80 87: 2*1+4*7+5*10 = 80 88: 2*10+4*0+5*12 = 80 89: 2*8+4*1+5*12 = 80 90: 2*6+4*2+5*12 = 80 91: 2*4+4*3+5*12 = 80 92: 2*2+4*4+5*12 = 80 93: 2*0+4*5+5*12 = 80 94: 2*5+4*0+5*14 = 80 95: 2*3+4*1+5*14 = 80 96: 2*1+4*2+5*14 = 80 97: 2*0+4*0+5*16 = 80 4*x1+5*x2+9*x3 = 80 22 solutions found. 1: 4*0+5*16+9*0 = 80 2: 4*5+5*12+9*0 = 80 3: 4*10+5*8+9*0 = 80 4: 4*15+5*4+9*0 = 80 5: 4*20+5*0+9*0 = 80 6: 4*4+5*11+9*1 = 80 7: 4*9+5*7+9*1 = 80 8: 4*14+5*3+9*1 = 80 9: 4*3+5*10+9*2 = 80 10: 4*8+5*6+9*2 = 80 11: 4*13+5*2+9*2 = 80 12: 4*2+5*9+9*3 = 80 13: 4*7+5*5+9*3 = 80 14: 4*12+5*1+9*3 = 80 15: 4*1+5*8+9*4 = 80 16: 4*6+5*4+9*4 = 80 17: 4*11+5*0+9*4 = 80 18: 4*0+5*7+9*5 = 80 19: 4*5+5*3+9*5 = 80 20: 4*4+5*2+9*6 = 80 21: 4*3+5*1+9*7 = 80 22: 4*2+5*0+9*8 = 80 12*x1+9*x2+7*x3 = 60 4 solutions found. 1: 12*5+9*0+7*0 = 60 2: 12*2+9*4+7*0 = 60 3: 12*1+9*3+7*3 = 60 4: 12*0+9*2+7*6 = 60 4*x1+6*x2+10*x3 = 100 51 solutions found. 1: 4*1+6*16+10*0 = 100 2: 4*4+6*14+10*0 = 100 3: 4*7+6*12+10*0 = 100 4: 4*10+6*10+10*0 = 100 5: 4*13+6*8+10*0 = 100 6: 4*16+6*6+10*0 = 100 7: 4*19+6*4+10*0 = 100 8: 4*22+6*2+10*0 = 100 9: 4*25+6*0+10*0 = 100 10: 4*0+6*15+10*1 = 100 11: 4*3+6*13+10*1 = 100 12: 4*6+6*11+10*1 = 100 13: 4*9+6*9+10*1 = 100 14: 4*12+6*7+10*1 = 100 15: 4*15+6*5+10*1 = 100 16: 4*18+6*3+10*1 = 100 17: 4*21+6*1+10*1 = 100 18: 4*2+6*12+10*2 = 100 19: 4*5+6*10+10*2 = 100 20: 4*8+6*8+10*2 = 100 21: 4*11+6*6+10*2 = 100 22: 4*14+6*4+10*2 = 100 23: 4*17+6*2+10*2 = 100 24: 4*20+6*0+10*2 = 100 25: 4*1+6*11+10*3 = 100 26: 4*4+6*9+10*3 = 100 27: 4*7+6*7+10*3 = 100 28: 4*10+6*5+10*3 = 100 29: 4*13+6*3+10*3 = 100 30: 4*16+6*1+10*3 = 100 31: 4*0+6*10+10*4 = 100 32: 4*3+6*8+10*4 = 100 33: 4*6+6*6+10*4 = 100 34: 4*9+6*4+10*4 = 100 35: 4*12+6*2+10*4 = 100 36: 4*15+6*0+10*4 = 100 37: 4*2+6*7+10*5 = 100 38: 4*5+6*5+10*5 = 100 39: 4*8+6*3+10*5 = 100 40: 4*11+6*1+10*5 = 100 41: 4*1+6*6+10*6 = 100 42: 4*4+6*4+10*6 = 100 43: 4*7+6*2+10*6 = 100 44: 4*10+6*0+10*6 = 100 45: 4*0+6*5+10*7 = 100 46: 4*3+6*3+10*7 = 100 47: 4*6+6*1+10*7 = 100 48: 4*2+6*2+10*8 = 100 49: 4*5+6*0+10*8 = 100 50: 4*1+6*1+10*9 = 100 51: 4*0+6*0+10*10 = 100 diophantine_3d_positive_test diophantine_3d_positive returns the positive solutions of a Diophantine equation in three variables. 6*x1+15*x2+10*x3 = 60 0 solutions found. 5*x1+3*x2+7*x3 = 24 1 solutions found. 1: 5*1+3*4+7*1 = 24 2*x1+4*x2+5*x3 = 80 65 solutions found. 1: 2*33+4*1+5*2 = 80 2: 2*31+4*2+5*2 = 80 3: 2*29+4*3+5*2 = 80 4: 2*27+4*4+5*2 = 80 5: 2*25+4*5+5*2 = 80 6: 2*23+4*6+5*2 = 80 7: 2*21+4*7+5*2 = 80 8: 2*19+4*8+5*2 = 80 9: 2*17+4*9+5*2 = 80 10: 2*15+4*10+5*2 = 80 11: 2*13+4*11+5*2 = 80 12: 2*11+4*12+5*2 = 80 13: 2*9+4*13+5*2 = 80 14: 2*7+4*14+5*2 = 80 15: 2*5+4*15+5*2 = 80 16: 2*3+4*16+5*2 = 80 17: 2*1+4*17+5*2 = 80 18: 2*28+4*1+5*4 = 80 19: 2*26+4*2+5*4 = 80 20: 2*24+4*3+5*4 = 80 21: 2*22+4*4+5*4 = 80 22: 2*20+4*5+5*4 = 80 23: 2*18+4*6+5*4 = 80 24: 2*16+4*7+5*4 = 80 25: 2*14+4*8+5*4 = 80 26: 2*12+4*9+5*4 = 80 27: 2*10+4*10+5*4 = 80 28: 2*8+4*11+5*4 = 80 29: 2*6+4*12+5*4 = 80 30: 2*4+4*13+5*4 = 80 31: 2*2+4*14+5*4 = 80 32: 2*23+4*1+5*6 = 80 33: 2*21+4*2+5*6 = 80 34: 2*19+4*3+5*6 = 80 35: 2*17+4*4+5*6 = 80 36: 2*15+4*5+5*6 = 80 37: 2*13+4*6+5*6 = 80 38: 2*11+4*7+5*6 = 80 39: 2*9+4*8+5*6 = 80 40: 2*7+4*9+5*6 = 80 41: 2*5+4*10+5*6 = 80 42: 2*3+4*11+5*6 = 80 43: 2*1+4*12+5*6 = 80 44: 2*18+4*1+5*8 = 80 45: 2*16+4*2+5*8 = 80 46: 2*14+4*3+5*8 = 80 47: 2*12+4*4+5*8 = 80 48: 2*10+4*5+5*8 = 80 49: 2*8+4*6+5*8 = 80 50: 2*6+4*7+5*8 = 80 51: 2*4+4*8+5*8 = 80 52: 2*2+4*9+5*8 = 80 53: 2*13+4*1+5*10 = 80 54: 2*11+4*2+5*10 = 80 55: 2*9+4*3+5*10 = 80 56: 2*7+4*4+5*10 = 80 57: 2*5+4*5+5*10 = 80 58: 2*3+4*6+5*10 = 80 59: 2*1+4*7+5*10 = 80 60: 2*8+4*1+5*12 = 80 61: 2*6+4*2+5*12 = 80 62: 2*4+4*3+5*12 = 80 63: 2*2+4*4+5*12 = 80 64: 2*3+4*1+5*14 = 80 65: 2*1+4*2+5*14 = 80 4*x1+5*x2+9*x3 = 80 14 solutions found. 1: 4*4+5*11+9*1 = 80 2: 4*9+5*7+9*1 = 80 3: 4*14+5*3+9*1 = 80 4: 4*3+5*10+9*2 = 80 5: 4*8+5*6+9*2 = 80 6: 4*13+5*2+9*2 = 80 7: 4*2+5*9+9*3 = 80 8: 4*7+5*5+9*3 = 80 9: 4*12+5*1+9*3 = 80 10: 4*1+5*8+9*4 = 80 11: 4*6+5*4+9*4 = 80 12: 4*5+5*3+9*5 = 80 13: 4*4+5*2+9*6 = 80 14: 4*3+5*1+9*7 = 80 12*x1+9*x2+7*x3 = 60 1 solutions found. 1: 12*1+9*3+7*3 = 60 4*x1+6*x2+10*x3 = 100 34 solutions found. 1: 4*3+6*13+10*1 = 100 2: 4*6+6*11+10*1 = 100 3: 4*9+6*9+10*1 = 100 4: 4*12+6*7+10*1 = 100 5: 4*15+6*5+10*1 = 100 6: 4*18+6*3+10*1 = 100 7: 4*21+6*1+10*1 = 100 8: 4*2+6*12+10*2 = 100 9: 4*5+6*10+10*2 = 100 10: 4*8+6*8+10*2 = 100 11: 4*11+6*6+10*2 = 100 12: 4*14+6*4+10*2 = 100 13: 4*17+6*2+10*2 = 100 14: 4*1+6*11+10*3 = 100 15: 4*4+6*9+10*3 = 100 16: 4*7+6*7+10*3 = 100 17: 4*10+6*5+10*3 = 100 18: 4*13+6*3+10*3 = 100 19: 4*16+6*1+10*3 = 100 20: 4*3+6*8+10*4 = 100 21: 4*6+6*6+10*4 = 100 22: 4*9+6*4+10*4 = 100 23: 4*12+6*2+10*4 = 100 24: 4*2+6*7+10*5 = 100 25: 4*5+6*5+10*5 = 100 26: 4*8+6*3+10*5 = 100 27: 4*11+6*1+10*5 = 100 28: 4*1+6*6+10*6 = 100 29: 4*4+6*4+10*6 = 100 30: 4*7+6*2+10*6 = 100 31: 4*3+6*3+10*7 = 100 32: 4*6+6*1+10*7 = 100 33: 4*2+6*2+10*8 = 100 34: 4*1+6*1+10*9 = 100 diophantine_3d_test(): Normal end of execution. 28-Jul-2021 00:29:07