show that any positive odd number is of the form 6q+1, 6q+3or 6q+5 where q is an integer
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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.
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