Question

$\huge \fbox \red{❥ Question}$
Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.
✳️gud luck XD..​

Answer 1

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.

Answer 2

Answer:$\huge \fbox \red{❥ Question}$Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.

$\huge\mathcal{\fcolorbox{lime}{black}{\pink{Answer}}}$

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