6. Prove that one and only one out of n, (n + 2) and (n + 4) is divisible by 3 where, n is any positive integer.
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Here is your answer.
Step-by-step explanation:
Let a be any positive number,b=3
By Euclid division lemma
a=bq+r, r<=0<b
a=3q+r,r=0,1,2
a=3q,3q+1,3q+2
If a=3q,
n=3q is divisible by 3
n+2=3q+2 is not divisible by 3
n+4=3q+4 is not divisible by 3
If a=3q+1,
n=3q+1 is not divisible by 3
n+2=3q+3 is divisible by 3
n+4=3q+5 is not divisible by 3
If a=3q+2,
n=3q+2 is not divisible by 3
n+2=3q+4 is not divisible by 3
n+4=3q+6 is divisible by 3
One and only one out of n,n+2,n+4 is divisible by 3
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