show that one and only one n,n+2,n+4 is divisible by 3
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let n be any positive integer and b=3n =3q+rwhere q is the quotient and r is the remainder0_ <r<3so the remainders may be 0,1 and 2so n may be in the form of 3q, 3q=1,3q+2
CASE-1
IF N=3qn+4=3q+4n+2=3q+2here n is only divisible by 3
CASE 2if n = 3q+1n+4=3q+5n+2=3q=3here only n+2 is divisible by 3
CASE 3IF n=3q+2n+2=3q+4n+4=3q+2+4=3q+6here only n+4 is divisible by 3
HENCE IT IS JUSTIFIED THAT ONE AND ONLY ONE AMONG n,n+2,n+4 IS DIVISIBLE BY 3 IN EACH CASE
let n be any positive integer and b=3n =3q+rwhere q is the quotient and r is the remainder0_ <r<3so the remainders may be 0,1 and 2so n may be in the form of 3q, 3q=1,3q+2
CASE-1
IF N=3qn+4=3q+4n+2=3q+2here n is only divisible by 3
CASE 2if n = 3q+1n+4=3q+5n+2=3q=3here only n+2 is divisible by 3
CASE 3IF n=3q+2n+2=3q+4n+4=3q+2+4=3q+6here only n+4 is divisible by 3
HENCE IT IS JUSTIFIED THAT ONE AND ONLY ONE AMONG n,n+2,n+4 IS DIVISIBLE BY 3 IN EACH CASE
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