Question

Show that every positive odd integer is of the form 8q+1,8q+3,8q+5,8q+7 ?

Answer 1

b=8
a=bq+r
0<=r<b
0<=r<8
possible remainders are 0,1,2,3,4,5,6,7
r=0
a=8q
r=1
a=8q+1 ✓
r=2
a=8q+2
r=3
a=8q+3 ✓
r=4
a=8q+4
r=5
a=8q+5 ✓
r=6
a=8q+6
r=7
a=8q+7 ✓
therefore every positive odd integer is of the form 8q+1,8q+3,8q+5,8q+7 .
I hope it is useful for you
pls make this answer as brainlist .....

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