
TL;DR
This paper identifies all integer values for which specific quadratic polynomials are smooth with respect to certain bounds, employing a method developed by Luca and the author.
Contribution
It determines all solutions where these quadratic polynomials are 200-smooth or 100-smooth, expanding understanding of smooth values of quadratic polynomials.
Findings
All x such that x^2+1, x^2+4, x^2+2, x^2-2 are 200-smooth are found.
All x such that x^2-4 is 100-smooth are identified.
The method of Luca and the author is applied to solve these smoothness problems.
Abstract
In this paper, using a method of Luca and the author, we find all values such that the quadratic polynomials and are 200-smooth and all values such that the quadratic polynomial is 100-smooth.
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