# How do you show that the sequence #11, 111, 1111, 11111,...# contains no perfect square number ?

##### 1 Answer

#### Answer:

If any of these numbers is square then it is the square of

Both

#### Explanation:

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Note that all of these numbers are of the form

**Suppose #n^2 = 100m+11# for some integers #m# and #n#**

Let

Then

Look at this modulo

We require

But

So neither value of

So our initial supposition is incorrect and there is no