show that only one of every three consecutive postive integers is divisible by 3 .
fast i need the answer very urgent !
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Answer:
Step-by-step explanation:
let the no .be (n-1,n,n+1,)
b=3 r = 0,1,2
a=bq+r (bq=n)
case 1 n-1
a= 3q-1 [r=0]
a= 3q+1-1=3q=3m [r=1] [q=m][divisible by 3]
a=3q+2-1=3q-1 [r=2]
case 2 n
a=3q=3m [r=0] [m=q][divisible by 3]
a=3q+1 [r=1]
a=3q+2 [r=2]
case3 n+1
a= 3q+1 [r=0]
a=3q+1+1=3q+2 [r=1]
a=3q+2+1=3q+3=3(q+1)=3m [r=2] [m=q+1][divisible by 3]
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