Question

2. Show that any positive odd integer is of the form 6q+1. or 69 +3, or 64 +5, where is
some integer​

Answer 1

Answer:

Let 'x' be any positive integer and b = 6

From Euclid's division lemma ,

a= bq+r

where 0<r<b.

Therefore , r can be 0,1,2,3,4,5

so all possible cases are,

a= 6q , a= 6q+1 , a= 6q+2

a= 6q + 3 , a= 6q +4 and a = 6q+5

But ,

a= 6q ,a= 6q+2, a= 6q +4 are all even cases.

So,

a= 6q+1, a= 6q + 3, a = 6q+5 are all odd cases and any positive odd integer are of these forms.

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