Question

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

Answer 1

Answer:

Step-by-step explanation:

a= bq+r where a is an odd positive integer

Where 0 <=r <b

Let b=6

Then a = 6q ,6q+1,6q+2,6q+3,6q+4,6q+5

But 6q,6q+2,6q+4 are even so

a= 6q+1, 6q+3 ,6q+5

Answer 2

Heya beautiful

Here is your answer

Let a be the positive odd integer which when divided by 6 gives q as quotient and r as remainder.

according to Euclid's division lemma

a=bq+r

a=6q+r

where , a=0,1,2,3,4,5

then,

a=6q

or

a=6q+1

or

a=6q+2

or

a=6q+3

or

a=6q+4

or

a=6q+5

but here,

a=6q+1 & a=6q+3 & a=6q+5 are odd.

Thanks mark me brainest