Question

Use euclid division lemma to show that any positive odd integer is of the form 6q + 1, or 6q + 3 or 6q + 5, where q is some integers

Answer 1

SOLUTION :

Let ' a ' be any positive odd integer.

Here, b = 6 ( from ques. )

Also,

We know that,

• BY EUCLID'S DIVISION LEMMA :

➡ a = bq + r,

$where \: r \leqslant 0 < d$

■ POSSIBLE VALUES OF ' r ' :-

• 0, 1, 2, 3, 4 and 5

Now,

Case : 1

a = 6q + 0

or

a = 6q ___________ [ Even ]

Case : 2

a = 6q + 1____________ [ Odd ]

Case : 3

a = 6q + 2 _____________ [ Even ]

Case : 4

a = 6q + 3 _____________ [ Odd ]

Case : 5

a = 6q + 4 _______________ [ Even ]

Case : 6

a = 6q + 5 _________________ [ Odd ]

From above, It's clear that any positive odd integer is of the form 6q + 1, 6q + 3 or 6q + 5.

$\rule{200}2$

Answer 2

Answer:

Hope it helps you

please mark brainliest