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We investigate the function $$P_{a,b;N}(\ell )$$ describing the number of $$\ell $$ -th powers among the first N terms of an arithmetic progression $$ax+b$$ . We completely describe the arithmetic… Click to show full abstract
We investigate the function $$P_{a,b;N}(\ell )$$ describing the number of $$\ell $$ -th powers among the first N terms of an arithmetic progression $$ax+b$$ . We completely describe the arithmetic progressions containing the most $$\ell $$ -th powers asymptotically. Based on these results we formulate problems concerning the maximum of $$P_{a,b;N}(\ell )$$ , and we give affirmative answers to these questions for certain small values of $$\ell $$ and N.
Keywords:
powers arithmetic;
arithmetic progressions
Journal Title: Ramanujan Journal
Year Published: 2021
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Journal Title: Ramanujan Journal
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!