Question

show that one and only one outof n, n+2,n+4 is divisible by3 where n is any positive integer​

Answer 1

Answer:

Step-by-step explanation:

let n be any positive integer and b=3

by euclids division lemma

n=bq +r,where 0≤r>b and b=3

n=3q+r

so r=0,1,2

so n may be of the form 3q,3q+1,3q+2

put r=0

n=3q

n+2=3q+2

n+4=3q+4

here here n is only divisible by 3

when r=1

n=3q+1

n+2=3q+1+2=3q+3

n+4=3q+1+4=3q+5

here n+2 is divisible by 3

when r=2

n=3q+2

n+2=3q+2+2=3q+4

n+4=3q+2+4=3q+6

here  n is only divisible by 3

Hence it is proved one and only one out of n,n+2,n+4 is divisible by 3

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