Czechoslovak Mathematical Journal, Vol. 73, No. 1, pp. 151-176, 2023
A Diophantine equation involving special prime numbers
Stoyan Dimitrov
Received December 16, 2021. Published online October 20, 2022.
Abstract: Let $[{\cdot}]$ be the floor function. In this paper, we prove by asymptotic formula that when $1<c<\frac{3441}{2539}$, then every sufficiently large positive integer $N$ can be represented in the form $N=[p^c_1]+[p^c_2]+[p^c_3]+[p^c_4]+[p^c_5],$ where $p_1$, $p_2$, $p_3$, $p_4$, $p_5$ are primes such that $p_1=x^2 + y^2 +1$.
Keywords: Diophantine equation; prime; exponential sum; asymptotic formula
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Affiliations: Stoyan Dimitrov, Technical Univesity of Sofia 1000, 8 Kl. Ohridski Blvd, Bulgaria, e-mail: sdimitrov@tu-sofia.bg
