Question

Show that the square of an positive odd integer cannot in the form of 6q +1 or 6q+5 for some integer q

Answer 1

Answer:

Here's your answer.

Step-by-step explanation:

Let is take the positive odd integer q=3.

So,

${q}^{2} = 6q + 1$

${3}^{2} = 6(3) + 1$

$9 < 19$

This states that 9 and 19 are not equal.

${q}^{2} = 6q + 5$

${3}^{2} = 6(3) + 5$

$9 < 23$

Even this statement states that 9 and 23 are not equal.

Hence, we can conclude that any positive odd integer can be greater than the equation 6q+1 and 6q+5 where q is an positive odd integer.