Question

show that any positive odd integer is of form 8q+1 or 8q+3 or 8q+5 or 8q+7​

Answer 1

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

Answer 2

Step-by-step explanation:

a = bq+r where, 0 <= r < b

so all possible values of a if b = 8

a = 8q+0, 8q+1, 8q+2, 8q+3, 8q+4, 8q+5, 8q+6, 8q+7

as it is asked for all odd values:

8q+0, 8q+2, 8q+4, 8q+6 will not be included as all these are even values

so answer will be:

a = 8q+1, 8q+3, 8q+5, 8q+7