Question

Can anyone solve the 2nd question

Answer 1

To show that any positive odd integer is

To show that any positive odd integer isof the from 6q+1, 6q+3, 6q+5 where q is

To show that any positive odd integer isof the from 6q+1, 6q+3, 6q+5 where q issome integer

Here is your answer:

By Euclid division algorithm,

We know that a = bq +r,0 <r <b

Let a be any positive integer and b = 6

Then, by Euclid's algorithm, a = 6q+r for some

integer q>0,

and r = 0, 1, 2, 3, 4, 5, or 0<r<6

Therefore, a = 6 or 6q+1 or 6 + 2 or 69 + 3 or

6q + 4 or 6q+5

A 6q +0:6 is divisible by 2,

it is an even number.

A6q+1:6 is divisible by 2, but 1 is not divisible

by 2

it is an odd number.

Therefore,

any odd integer can be expressed in the form

6q+1 or 6q + 3 or 6q+5

Hence proved.

I hope it helps you and if you appreciate

I hope it helps you and if you appreciatemy answer, please do respond with a

I hope it helps you and if you appreciatemy answer, please do respond with athanks.

Answer 2

Answer:

To show that any positive odd integer is

To show that any positive odd integer isof the from 6q+1, 6q+3, 6q+5 where q is

To show that any positive odd integer isof the from 6q+1, 6q+3, 6q+5 where q issome integer

Here is your answer:

By Euclid division algorithm,

We know that a = bq +r,0 <r <b  

Let a be any positive integer and b = 6

Then, by Euclid's algorithm, a = 6q+r for some  

integer q>0,  

and r = 0, 1, 2, 3, 4, 5, or 0<r<6

Therefore, a = 6 or 6q+1 or 6 + 2 or 69 + 3 or  

6q + 4 or 6q+5  

A 6q +0:6 is divisible by 2,  

it is an even number.

A 6q+1:6 is divisible by 2, but 1 is not divisible

by 2  

it is an odd number.  

Therefore,  

any odd integer can be expressed in the form

6q+1 or 6q + 3 or 6q+5

Hence proved.

Step-by-step explanation:

Thanks..!