5 Assuming that there are two square integers whose ratio is

5. Assuming that there are two square integers whose ratio is 5, derive a contradiction using the principle that underlies Knorr’s conjecture. (If the integers are relatively prime, then both must be odd. Use that fact and the fact that the square of any odd number is one unit larger than a multiple of 8 to derive a contradiction.)

Solution

Let\'s assume one integer is p.

then another is 5p because ratio is 5.

Now, Let\'s assume p is even. it means it is devisible by 2.

Then 5p is also even.

Now, p and 5p are both even. Then they can not be relatively prime which is a contradiction because there is such a number except one which devides both of them simultaneously and that is 2.

So, p can\'t be even.

So p must be odd and that of 5p will be odd. So both of them must be odd.