How do you show that the sequence 11, 111, 1111, 11111,... contains no perfect square number ?
1 Answer
Jul 16, 2015
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
Let
Then
Look at this modulo
We require
But
So neither value of
So our initial supposition is incorrect and there is no