Abstract
We use the theory of exponent pairs and Vaaler polynomials to show that any interval of the form $[x,x+x^{1/2}]$ contains an integral multiple $m^2r \in [x,x+x^{1/2}]$ of a perfect square $m^2$ with an integer $m > x^{0.281286}$.
Citation
Joël Rivat. Igor E. Shparlinski. "Multiples of squares in short intervals." Funct. Approx. Comment. Math. 54 (1) 57 - 63, March 2016. https://doi.org/10.7169/facm/2016.54.1.5
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