Question

use the euclids division lemmo to show that any +ve odd integer is one of the form 6q+1 or 6q+3 or 6q+5, is an integer plzz answer this question​

Answer 1

We know that

a= bq +r where 0≤r<b

let b = 6

then

a = 6q+ r where 0≤r<6

r = 0,1,2,3,4,5

when r=0. a = 6q -----------> even

r=1. a= 6q +1----------> odd

r = 2. a= 6q + 2 ---------> even

r=3. a= 6q+ 3 -------------> odd

r=4 a= 6q + 4 ---------------> even

r=5 a= 6q+ 5 -------------> odd

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

Hope helpful