Question

show that any positive integer in the form of 6q or 6q + 2 or 6q + 4 where Q is some integer

Answer 1

Let a be any positive integer
and b = m
r = 0 ,1, 2,3,4,5
according to Euclid division lemma...
a = bq+ r
so,
a =6m
sq on both sides
a2 = 36m2
= 6(6m2)
=6q (where q = 6m2)

a = 6m +1
sq on both side
=36m2 +12m +1
=6 (6m2 +2m) +1
=6q+1 (where q = m2 +2m )

a= 6m+2
sq on both side
=36m2 + 24m + 4
=6 (6m2 + 4m) +4
=6q + 4 (where q= 6m2 + 4m)