Question

Use Euclid's division lemma to show that every odd integer is of the form 2p + 1​

Answer 1

Answer:

Step-by-step explanation:

Answer:-

Let a be a positive odd integer

a=bq+r

b=6

a=6q+r, 0≤r<6. So,the possible values of r are 0,1,2,3,4,5

Set of positive odd integers are {1,3,5,7,9......}

put a=1,3,5,7,9......

a=bq+r

1=6(0)+1=6q+1 [r=1]

3=6(0)+3=6q+3 [r=3]

5=6(0)+5=6q+5 [r=5]

7=6(1)+1=6q+1 [r=1]

9=6(1)+3=6q+3 [r=3]

So,any positive integer is of the form 6q+1,6q+3,6q+5 where q is certain integer.

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