Question

Show that any positive odd integers. 1 is of the from6q+1 or6q+5,6q+3 where q is some integer​

Answer 1

Answer:

Step-by-step explanation:

Let a be an integer.

According to lemma 0<=r<b , here b=6 and a =bq+r

So the possible remainders are 0,1,2,3,4and 5.

When r=0 , a= 6q ( for some integer q)

r=1, a=6q+1

r=2,a=6q+2

r=3,a =6q+3

r=4,a =6q+4

r=5,a=6q+5

So , any positive odd integer is of the form 6q+1,6q+3 or 6q+5 for some integer q.

Answer 2

Answer:

0<r<6 the po possible possible reminders are 0,1,2,3,4,5

Step-by-step explanation:

1=6(0)+(1)=6q+1

3=6(0)+(3)=6q+3

5=6(0)+(5)=6q+5

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