## 2. Use Euclid division lemma to show that any positive odd integer is of the form 6q+1, or 69 + 3 or 6q+5, where is some integers.

Question

2.
Use Euclid division lemma to show that any positive odd integer is of the form 6q+1, or
69 + 3 or 6q+5, where is some integers.
the for​

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4 weeks 2021-11-02T05:10:20+00:00 2 Answers 0 views 0

1. Heya,

Use Euclid’s division lemma to show that any positive odd integer is of the form 6q+1,6q+3,6q+5 where q is a certain integer.

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.

Hence showed.

Hope it helps