Math, asked by Ashliey4, 11 months ago

Show that exactly one of the numbers n, n+2 or n+4 is divisible by 4.

Answers

Answered by MagicalGiggles

$<body bgcolor=b>$

$\huge\mathbb\pink{DULARI..!!}$

$<font color = white>$

By Euclid Division Lemma

If a and b are 2 positive integers then

a = bq + r [ Where 0 ≤ r < b ]

If b = 3

a = 3q + r

[ Where 0 ≤ r < 3 ]

r = 0 , 1 , 2

:. Numbers = 3q + 0 , 3q + 1 , 3q + 2

Let ,

n = 3q , 3q + 1 , 3q + 2

⭐ If n = 3q

➡️n = 3q

n is divisible by 3

➡️ n + 2 = 3q + 2

n + 2 = 3(1) + 2 = 5

5 is not divisible by 3

:. n + 2 is not divisible by 3

➡️ n + 4 = 3q + 4

n + 4 = 3(1) + 4 = 7

7 is not divisible by 3

:. n + 4 is not divisible by 3

⭐ If n = 3q + 1

↘️n = 3q + 1

n = 3(1) + 1 = 4

4 is not divisible by 3

:. n is not divisible by 3

↘️n + 2 = 3q + 1 + 2

n + 2 = 3(2) + 3

n + 2 = 3(q + 1)

:. n + 2 is divisible by 3

↘️n + 4 = 3q + 1 + 4 = 3q + 5

n + 4 = 3(1) + 5 = 8

8 is not divisible by 3

:. n + 4 is not divisible by 3

⭐If n = 3q + 2

♦️n = 3q + 2

n = 3(1) + 2 = 5

5 is not divisible by 3

:. n is not divisible by 3

♦️n + 2 = 3q + 2 + 2 = 3q + 4

n + 2 = 3(1) + 4 = 7

7 is not divisible by 3

:. n + 2 is not divisible by 3

♦️ n + 4 = 3q + 2 + 4 = 3q + 6

n + 4 = 3(q + 2)

:. n + 4 is divisible by 3

$<marquee>♓DULARI♓</marquee>$

Previous Question

Next Question