Question

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=b q+r )
( a=6 q+r )
where ( , a=0,1,2,3,4,5 )
then,
( a=6 q )
Or
( a=6 q+1 )
Or
( a=6 q+2 )
Or
( a=6 q+3 )
Or
( a=6 q+4 )
Or
( a=6 q+5 )
but here, ( a=6 q+1 & a=6 q+3 & a=6 q+5 ) are odd

# 3. W 20 Show that any positive odd integer is of the from 69 + 1, or 64+3, or 64+5, where q is some integer.

Solution