Question

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

Answer 1

Answer:

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Answer 2

Answer:

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

.$\huge \fbox \red{❥ AnSwEr}$

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=bx+r

a=6x+r

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

then,

a=6x

or

a=6x+1

or

a=6x+2

or

a=6x+3

or

a=6x+4

or

a=6x+5

but here,

a=6x+1 & a=6x+3 & a=6x+5 are odd