Geodesic
A diophantine equation involving special prime numbers
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 1, pp. 151-176 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $[{\cdot }]$ be the floor function. In this paper, we prove by asymptotic formula that when $1
Let $[{\cdot }]$ be the floor function. In this paper, we prove by asymptotic formula that when $1$, 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 $p_1=x^2 + y^2 +1$.
DOI : 10.21136/CMJ.2022.0469-21
Classification : 11L07, 11L20, 11P32
Keywords: Diophantine equation; prime; exponential sum; asymptotic formula 
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Dimitrov, Stoyan. A diophantine equation involving  special prime numbers. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 1, pp. 151-176. doi: 10.21136/CMJ.2022.0469-21

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