On the Győry-Sárközy-Stewart conjecture in function fields
Igor E. Shparlinski (2018)
Czechoslovak Mathematical Journal
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We consider function field analogues of the conjecture of Győry, Sárközy and Stewart (1996) on the greatest prime divisor of the product for distinct positive integers , and . In particular, we show that, under some natural conditions on rational functions , the number of distinct zeros and poles of the shifted products and grows linearly with if . We also obtain a version of this result for rational functions over a finite field.