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INDICATII #3237 GCDnot1

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Jan 5th, 2020
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  1. INDICATII #3237 GCDnot1
  2.  
  3. Se completează o matrice c cu numere prime astfel încât c[i][j] este un număr prim cu care sunt divizibile numerele a+i şi b+j.
  4. Când elementul c[i][j] primeşte ca valoare un anumit număr prim p, se vor completa în matricea c, cu acelaşi număr prim şi elementele de forma c[i+p*k][j+p*k], unde k este orice număr întreg pentru care indicii respectivi există.
  5. Se determină apoi, utilizând lema chinezească a resturilor, un număr a care verifică congruenţele a+i≡0(mod c[i][u]) pentru orice i=0,m-1, şi orice u=0,n-1.
  6. Se determină apoi, utilizând lema chinezească a resturilor, un număr b care verifică congruenţele b+j≡0(mod c[u][j]) pentru orice u=0,m-1, şi orice j=0,n-1.
  7.  
  8. m=1 si n=2
  9. a=6 si b=14
  10. ......................
  11. m=1 si n=3
  12. a=14=2*7 si b=6 ( 7, 8) (b+1, b+2)
  13. .................................
  14. m=1 si n=4
  15. a=42=2*3*7 si b=6 ( 7, 8, 9) (b+1, b+2, b+3)
  16. ...........................................
  17. m=1 si n=5
  18. a=2*3*7=42 si b=6 (7, 8, 9, 10) (b+1, b+2, b+3, b+4)
  19. m=1 si n=6
  20. a=2*3*7*11=462 si b=6 (7, 8, 9, 10, 11) (b+1, b+2, b+3, b+4, b+5)
  21. ....................................................................
  22. m=1 si n=7
  23. a=2*3*7*11=462 b=6, (7, 8, 9, 10, 11, 12) (b+1, b+2, b+3, b+4, b+5, b+6)
  24. ............................................................................
  25. m=1 si n=8
  26. a=2*3*7*11*13=6006 b=6, (7, 8, 9, 10, 11, 12, 13) (b+1, b+2, b+3, b+4, b+5, b+6, b+7)
  27. .......................................................................................
  28. m=1 si n=9
  29. a=2*3*7*11*13=6006 b=6, (7, 8, 9, 10, 11, 12, 13, 14) (b+1, b+2, b+3, b+4, b+5, b+6, b+7, b+8)
  30. ....................................................................................................
  31. m=1 si n=10
  32. a=2*3*7*11*13=6006 b=6, (7, 8, 9, 10, 11, 12, 13, 14, 15) (b+1, b+2, b+3, b+4, b+5, b+6, b+7, b+8, b+9)
  33. ...........................................................................................................
  34. m=1 si n=11
  35. a=2*3*7*11*13=6006 b=6, (7, 8, 9, 10, 11, 12, 13, 14, 15, 16) (b+1, b+2, b+3, b+4, b+5, b+6, b+7, b+8, b+9, b+10)
  36. ....................................................................................................................
  37. m=1 si n=12
  38. a=2*3*7*11*13*17=102102 b=6, (7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17) (b+1, b+2, b+3, b+4, b+5, b+6, b+7, b+8, b+9, b+10, b+11)
  39. ...................................................................................................................................
  40. m=1 si n=13
  41. a=2*3*7*11*13*17=102102 b=6, (7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18) (b+1, b+2, b+3, b+4, b+5, b+6, b+7, b+8, b+9, b+10, b+11, b+12)
  42. ...........................................................................................................................................
  43. m=1 si n=14
  44. a=2*3*7*11*13*17*19=1939938 b=6, (7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19) (b+1, b+2, b+3, b+4, b+5, b+6, b+7, b+8, b+9, b+10, b+11, b+12, b+13)
  45. ...............................................................................................................................................................
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