1.

Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q issome integer

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Answer:

Step-by-step explanation:

To Show :-

Any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5.

Solution :-

Let the GIVEN integer be a.

On dividing a by 6 , we GET q as the quotient and r as the remainder  

a = 6q + r

r = 0, 1, 2, 3, 4, 5

a = 6q , Even Number

when r = 1

a = 6q + 1, Odd Number

when r = 2

a = 6q + 2, Even Number

when r = 3

a=6q + 3, Odd Number

when r = 4

a=6q + 4, Even Number

when r = 5,

a= 6q + 5 , Odd Number

Hence Proved.

Any positive odd integer is of the form 6q + 1, 6q + 3 or 6q + 5.


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