Question

showthat every odd numberis in the formof 6q+1 or 6q+3 or 6q+5. (using euclid's division lemma)

Answer 1

as the euclid's division lemma every number can be expressed in the form of
a=bq+r,0 less than or equal to r less than b
according to the question the numbers are 6q ,6q+1 ,6q+2 ,..., 6q+5 since when a number is divided with 6 the remainders are 0,1,2,3,4,5
from the above the positive odd integers are 6q+1 ,6q+3 ,6q+5