Question

Use Euclid division lemma to show that any positive odd integer is of the form 6q+lor
69 + 3 or 69+5. where q is some integers.​

Answer 1

Step-by-step explanation:

latestlatest art with taking a very is a Porsche to integer or even integer we apply the division algorithm with a and b is equal to 660 less than or equal to or less than 6 the possible reminder 0 1 2 3 4 5 that is a can be 46 you are 6q + 1 or 6 plus two are 6q + 3 or 6q+ 4,6q+ 5 where q is the question however since there is even a cannot be for 4q+ 1 or 4q + 3 since they are both divisible by 2 and 3 therefore any even integer is can be written as 6q+3 or 6q+1,6q+5

Answer 2

Answer:

Let

′

a

′

be any positive integer and b=6

Then by division algorithm

a=6q+r where r=0,1,2,3,4,5

so, a is of the form 6q or 6q+1 or 6q+2 or 6q+3 or

6q+3 or 6q+4 or 6q+5

Therefore If s is an odd integer

Then

′

a

′

is of the form 6q+1 or 6q+3 6q+5

Hence a positive odd integer is of the form 6q+1 or 6q+3 or 6q+5