Question

Show that any positive odd integer is of the form 8q+1, or 8q+3, or 8q+5, or 8q+7, where q is some integer

Answer 1

Answer:

Step-by-step explanation:

Let a be any arbitrary positive odd integer.

When a is divided by 8, by euclid's division lemma,

a = bq + r

where r = 0,1,2,3,4,5,6,7

Since a is odd, therefore, every odd integer is of the form 8q+1 , 8q+3 , 8q+5 , 8q+7

Answer 2

Answer:

Yes

Let a be any positive integer

According to Euclids division lemma

a = bq + r

b = 8

so the possible values of r = 0,1,2,3,4,5,6,7

a = 8q ( it is even)

a = 8q + 1 ( it is odd)

..........and so on