Question

impartind numerele 1243,1437,2257 la un numar n,obtinem resturile 18,12 si respectiv 7.Aflati numarul n.

Answer 1

[tex]1243 = n*c_{1} + 18 1437 = n * c_{2} + 12 2257 = n* c_{3} + 7 \\ \\ 1243 - 18 = n*c_{1} \\ 1225 = n*c_{1} \\ \\ 1437 - 12 = n * c_{2} \\ 1425 = n*c_{2} \\ \\ 2257 - 7 = n *c_{3} \\ 2250 = n* c_{3} \\ \\ [/tex]

=>Divizori comuni ai lui 1225 , 1425 , 2250         , n > 18

D 1225 = { 5; 7; 25; 35; 49; 175; 245;1.225 }

D 1425 = { 1; 3; 5; 15; 19; 25; 57; 75; 95; 285; 475 }

D 2250={ 1; 2; 3; 5; 6; 9; 10; 15; 18; 25; 30; 45; 50; 75; 90; 125; 150; 225; 250; 375; 450; 750; 1.125 și 2.250}

D1125 ∩ D1425 ∩ D2250 [Unde n > 18] = { 25 }