sir, please help with this question show that the one and only number in n,n+2,n+4 which is divisible by 3
Asked by
| 17th Jun, 2011,
10:25: PM
To prove one of n, n+2 or n+4 is divisible by 3.
Case 1: Let n is divisible by 3
So n = 3k for some positive integer k
Now n+2 = 3k+2 which is not divisible by 3
n+4 = 3k +3+1 =3(k+1)+1 =3m+1 not divisible by 3
Case 2: n+2 is divisible by 3 so
n+2 =3k
so n =3k-2 not divisible by 3
n+4 = 3k+2 = not divisible by 3
Case 3: Let n+4 is divisible by 3 so n+4 = 3k
n =3k-4=3(k-1)-1=3m-1 not divisible by 3
n+2 = 3k-2 not divisible by 3
To prove one of n, n+2 or n+4 is divisible by 3.
Case 1: Let n is divisible by 3
So n = 3k for some positive integer k
Now n+2 = 3k+2 which is not divisible by 3
n+4 = 3k +3+1 =3(k+1)+1 =3m+1 not divisible by 3
Case 2: n+2 is divisible by 3 so
n+2 =3k
so n =3k-2 not divisible by 3
n+4 = 3k+2 = not divisible by 3
Case 3: Let n+4 is divisible by 3 so n+4 = 3k
n =3k-4=3(k-1)-1=3m-1 not divisible by 3
n+2 = 3k-2 not divisible by 3
Answered by
| 18th Jun, 2011,
04:20: PM
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