Prove that there are infinitely many perfect squares starting with 2018(as for example 20187049,201810436 are perfect square.
First of all I had assumed that there are finitely many perfect square numbers starting with 2018 and thought proving this by contradiction. Now let M is the maximum number starting with 2018. I can realize that we can find another number N\gt M which is a perfect square starting with 2018 . But I failed to find any direct method of solving this. Somebody please give any hint or the full solution.
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