1.

Show that only one out of a a+2 and a+4 is divisible by 3

Answer»

ANSWER:

Step-by-step explanation:

let a be any positive integer and b=3

a =3q+r

where q is the quotient and r is the remainder

0_

so the REMAINDERS may be 0,1 and 2

so a may be in the FORM of 3q, 3q=1,3q+2

CASE-1

IF A=3q

a+4=3q+4

a+2=3q+2

here a is only DIVISIBLE by 3

CASE 2

if a = 3q+1

a+4=3q+5

a+2=3q=3

here only a+2 is divisible by 3

CASE 3

IF a=3q+2

a+2=3q+4

a+4=3q+2+4

=3q+6

here only a+4 is divisible by 3

HENCE IT IS JUSTIFIED THAT ONE AND ONLY ONE AMONG a,a+2,a+4 IS DIVISIBLE BY 3 IN EACH CASE.

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