Math, asked by haribabumanthena2, 8 months ago

Show that one and only
positive integer
one out of n, n+2 or n + 4 is divisible by 3, where n is any​

Answers

Answered by sharmamanasvi007
0

Answer:

let n be any positive integer and b=3

n =3q+r

where q is the quotient and r is the remainder

0<r<3

so the remainders may be 0,1 and 2

so n may be in the form of 3q, 3q=1,3q+2

\underline{CASE-1}

IF N=3q

n+4=3q+4

n+2=3q+2

here n is only divisible by 3

\underline{CASE-2}

if n = 3q+1

n+4=3q+5

n+2=3q=3

here only n+2 is divisible by 3

\underline{CASE-3}

IF n=3q+2

n+2=3q+4

n+4=3q+2+4

=3q+6

here 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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