Question

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

Answer 1

let a be any positive integer,b=6

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

a=6q+r

therefore,

6q will be a positive even integer as 6 is an even no.and if we multiply an integer with an even no. the product will be also even

therefore,

6q,6q+2,6q+4 will be even and

6q+1,6q+3,6q+5eill be odd