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Integer coordinates (Posted on 2019-05-09) Difficulty: 3 of 5
On the graph y=(x-2019)2019-x2, how many points are there with integer coordinates?

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution solution | Comment 1 of 2
x values -44 through 44 produce integral values of the exponent and thus of y. This accounts for 89 points.

x=2020 makes the base 1. Even to a fractional power, it results in 1.

Zero would not work with a negative power so x=2019 is bad. 

x=2018 makes the base -1 and the power odd though negative, so y is -1

These latter values bring the total to 91.


  Posted by Charlie on 2019-05-09 14:18:54
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