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show that one and only one out of n,n+2,n+4 is divisible by 3 ,where n is any positive integer

Posted by Md Aarif 6 years, 5 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 6 years, 5 months ago

We applied Euclid Division algorithm on n and 3.
a = bq +r on putting a = n and b = 3
n = 3q +r , 0<r<3
i.e n = 3q -------- (1),n = 3q +1 --------- (2), n = 3q +2 -----------(3)
n = 3q is divisible by 3
or n +2 = 3q +1+2 = 3q +3 also divisible by 3
or n +4 = 3q + 2 +4 = 3q + 6 is also divisible by 3

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CBSE > Class 10 > Mathematics