CBSE Class 10 Answered
show that one and only one out of p, p+2 or p+4 is divisible by 3, where p is any positive integer.
Asked by Ritwika Sharma | 30 Aug, 2012, 07:53: PM
Expert Answer
To prove one of p, p+2 or p+4 is divisible by 3.
Case 1: Let p is divisible by 3
So p = 3k for some positive integer k
Now p+2 = 3k+2 which is not divisible by 3
p+4 = 3k +3+1 =3(k+1)+1 =3m+1 not divisible by 3
Case 2: p+2 is divisible by 3 so
p+2 =3k
so p =3k-2 not divisible by 3
p+4 = 3k+2 = not divisible by 3
Case 3: Let p+4 is divisible by 3 so p+4 = 3k
p =3k-4=3(k-1)-1=3m-1 not divisible by 3
p+2 = 3k-2 not divisible by 3
Answered by | 30 Aug, 2012, 10:43: PM
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