Irrationally, Can This Happen?

Number Theory Level 4

True or False?

The infinite sequence ⌊1×2017⌋, ⌊2×2017⌋, ⌊3×2017⌋, ⌊4×2017⌋, …\big\lfloor 1\times \sqrt{ 2017 } \big\rfloor,\ \big\lfloor 2 \times \sqrt{ 2017 } \big\rfloor,\ \big\lfloor 3 \times \sqrt{ 2017 } \big\rfloor,\ \big\lfloor 4 \times \sqrt{ 2017 } \big\rfloor,\ \ldots contains infinitely many perfect squares.


Notation: ⌊⋅⌋ \lfloor \cdot \rfloor denotes the floor function.

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Calvin Lin by Calvin Lin
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