Question

Use Euclid division lemma to show that the square of any postive integer cannot be of the form 5m + 2 or 5m + 3 for some integer m.​

Answer 1

Use Euclid division lemma to show that the square of any postive integer cannot be of the form 5m + 2 or 5m + 3 for some integer m.

Answer 2

Answer:-

The number we get will be 58.

Solution:-

Let:-

The digit at the unit place be b and the digit at the tenth place be a.

According to the question:-

We have:-

=> a + b = 13______(i)

As in the question it's not specified that which digit is greater either a or b so we have two cases :-

If a > b, Then Equation 2 we get will be

=> a - b = 3

Now upon adding these equation 1 & 2 we get

=> 2a = 16

=> a = 16/2

=> a = 8

And:-

=> b = a - 3

=> b = 8 - 3

=> b = 5

So:-

Here the number we get is 85.

If, a < b, then the equation 3 will be

=> b - a = 3

Now, upon adding equation 1 & 3 we get,

=> 2b = 16

=> b = 16/2

=> b = 8

And:-

=> a = b - 3

=> a = 8 - 3

=> a = 5

Therefore:-

Here the number we get will be 58.