Múltiplos de 3

Múltiplos de 3

1. m de 3

   • {0,3,6,9,12,15...}
     • 3n

2. m de 3+1

   • {1,4,7,10,13,16...
     • 3n+1

3. m de 3+2

   • {2,5,8,11,14,17...}
     • 3n+2

4. A=3n+1, n E N

   • B=3k+2 , k E N
     • A+B=3 (n+k+1)
       • P=3n+r
         • Q=3k+s
           • P+Q=3(n+k)+r+s
             • P*Q=(3n+r)(3k+s)
               • =9kn+3ns+3kr+rs
                 • 9kn+3ns+3kr=3Y
                 • 3Y+rs
                   • os restos se multiplicam
                     • 423/3 = (4/3)(100/3)+(2/3)(10/3)+(3/3)
                       • somando e multiplicando os restos
                         • (1*1)+(2*1)+0=3
                           • 3/3=0
       • A*B=(3n+1)(3n+2)=
         • =9n²+6n+3n+2
           • =9n²+9n+2
             • =3x+2

5. abc =3n

   • a+b+c=3x
     • abc=100a+10b+c
       • =(99a+9b)+a+b+c
         • 99a+9b= 3k
           • então a+b+c tem que ser igual á 3x\3x+3k=3n