Asked by SITHARA | 27th Mar, 2009, 07:55: PM
suppose pis divisible by 3
then p=3q (say) where q is some non negative integer.
the next multiple of 3 will be only p+3,p+6 etc( multiples of 3 will occur only after a gap pf 3)
So, if p is a multiple of 3 then p+2 and p+4 can't be multiples of 3
Next if p+2 is a multiple of 3 then p+2= 3r(say)
So, the multiple of 3 before p+2 must be (p+2)-3 and the next mutiple after p+2 will be (p+2)+3
i.e. p-1 and p+5 respectively. So if p+2 is a multiple of 3 then por p+4 can't be multiples of 3.
By a similar logice, we can show that if p+4 is a multiple of 3 then p or p+2 can't be multiples of 3.
This explains the answer.
Answered by | 27th Mar, 2009, 10:48: PM
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