Question

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

some integer.​

Answer 1

Answer:

here is your answer

Step-by-step explanation:

yessss any odd integer is of the form 6q+1, 6q+3, 6q+9

here is step be step explanation that is shown in answer...

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Answer 2

Answer:

Let n be any positive odd integer.

When n is divided by 6, let quotient be q and remainder be r, such that,

n=6q+r...... (1)

where, 0 < r <6.

So, r=0 or r=1 or r=2 or r=3 or r=4 or r=5.

Putting r=0 in (1)

n=6q+0

=6q

Here, n=6q, which is clearly even. So, no odd natural number can be of the form 6q.

Putting r=1 in (1)

n=6q+1

Here, n=6q+1, which is clearly odd. So, an odd natural number can be of the form 6q+1

Putting r=2 in (1)

n=6q+2

Here, n=6q+2, which is clearly even. So, no odd natural number can be of the form 6q+2.

Putting r=3 in (1)

n=6q+3

Here, n=6q+3, which is clearly odd. So, an odd natural number can be of the form 6q+3.

Putting r=4 in (1)

n=6q+4

Here, n=6q+4, which is clearly even. So, no odd natural number can be of the form 6q+4.

Putting r=5 in (1)

n=6q+5

Here, n=6q+5, which is clearly odd. So, an odd natural number can be of the form 6q+5.

*Hence, verified that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.*