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| 1. |
Show that exacty one of the numbers n,n+2 or n+4 is divisible by 3. |
| Answer» On dividing n by 3,let q be the quotient and r be the remainder Then n=3q+r where r is greater or equal to 0 and Lessthan 3n = 3q+r where r=0,1,2n =3q or 3q+1or 3q+2Case1 if n=3q then n is divisible by 3 Case2 if n=3q+1 then(n+2) =3q+3=3(q+1) which is divisible by3Case3 if n=3q+2 then (n+4) =3q+6=3(q+2) which is divisible by 3 Hence in all cases one any one out of n,n+2,n+4 is divisible by 3 | |