Question

1. Daca impartim nr nat nenul n la 9 si respectiv,14, se obtin resturile 8 si 9. Ce rest se obtine la impartirea lui n la 126???? DAU COROANA <3

Answer 1

n : 9 = c₁ rest 8
n= 9c₁ + 8

n : 14= c₂ rest 9
n=14c₂ + 9


n=9c₁ + 8     |(+19)
n=14c₂ + 9   |(+19)

n+19=9c₁+8+19    <=> n+19=9c₁+27
n+19=14c₂+9+19  <=> n+19=14c₂+28

n+19=9(c₁+3)
n+19=14(c₂+2)    ====> 9(c₁+3)=14(c₂+2)
                                  ---> {9|c₂+2
                                        {14|c₁+3  ===> c₁+3=14k
                                                                 c₂+2=9k   ;    k ∈ N*
n+19=9(c₁+3)
n+19=9*14k
n+19=126k    ===> n=126k-19
                               n=126k -126 +126 -19
                               n=126(k-1) + 107     ;    k-1=m
                         
                               n=126m + 107
Se poate observa ca restul impartirii numarului n la 126 este 107.