Question

show that any positive odd integer is of the form 6qplus 1 or 3 or 5

Answer 1

Answer:

let a be any positive integer and b=6. Then, by euclids algorithm, a=6q+r and 0<=r<6

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

a=6q

a=6q+1

a=6q+2

a=6q+3

a=6q+4

a=6q+5

here we can see that 6q, 6q+2, 6q+4 can not be positive odd integers because these are divisible by 2

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