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madhavchilukurp35nb1
@madhavchilukurp35nb1
July 2021
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Prove that one of the number n n+2 and n+4 is divisible by 3
Answers & Comments
KshitijMaurya
Heya
Here's ur answer
By Euclid's division Lemma any natural number can be written as:
B=aq+r
where r = 0, 1, 2,.........(a-1). and q is the quotient.
put a = 3: b = 3q+r and r = 0,1,2.
thus any number is in the form of 3q , 3q+1 or 3q+2.
case I: if n =3q
n is divisible by 3,
n+2 = 3q+2 is not divisible by 3.
n+4 = 3q+4 = 3(q+1)+1 is not divisible by 3.
case II: if n =3q+1
n = 3q+1 is not divisible by 3.
n+2 = 3q+1+2=3q+3 = 3(q+1) is divisible by 3.
n+4 = 3q+1+4 = 3q+5 = 3(q+1)+2 is not divisible by 3.
case III: if n = 3q+2
n =3q+2 is not divisible by 3.
n+2 = 3q+2+2 =3q+4 = 3(q+1)+1 is not divisible by 3.
n+4 = 3q+2+4 = 3q+6 = 3(q+2) is divisible by 3.
thus one and only one out of n , n+2, n+4 is divisible by 3.
Hence,proved that n+2 and n+4 are divisible by 3
HOPE IT HELPS U:-)
3 votes
Thanks 3
madhavchilukurp35nb1
Thanks a lot
madhavchilukurp35nb1
I needed ur help
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Answers & Comments
Here's ur answer
By Euclid's division Lemma any natural number can be written as:
B=aq+r
where r = 0, 1, 2,.........(a-1). and q is the quotient.
put a = 3: b = 3q+r and r = 0,1,2.
thus any number is in the form of 3q , 3q+1 or 3q+2.
case I: if n =3q
n is divisible by 3,
n+2 = 3q+2 is not divisible by 3.
n+4 = 3q+4 = 3(q+1)+1 is not divisible by 3.
case II: if n =3q+1
n = 3q+1 is not divisible by 3.
n+2 = 3q+1+2=3q+3 = 3(q+1) is divisible by 3.
n+4 = 3q+1+4 = 3q+5 = 3(q+1)+2 is not divisible by 3.
case III: if n = 3q+2
n =3q+2 is not divisible by 3.
n+2 = 3q+2+2 =3q+4 = 3(q+1)+1 is not divisible by 3.
n+4 = 3q+2+4 = 3q+6 = 3(q+2) is divisible by 3.
thus one and only one out of n , n+2, n+4 is divisible by 3.
Hence,proved that n+2 and n+4 are divisible by 3
HOPE IT HELPS U:-)