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

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Answer 2

Answer:

Explanation:

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