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JOURNALS // Chebyshevskii Sbornik // Archive

Chebyshevskii Sb., 2024 Volume 25, Issue 4, Pages 5–26 (Mi cheb1471)

The solution of some equation in primes

I. Allakov, N. S. Muzropova

Termez State University (Termez, Uzbekistan)

Abstract: The work proves that, under some additional conditions, every sufficiently large integer can be represented as the sum of two prime numbers and the square of a third prime number. A lower bound for the quantity of representation of a given integer in the specified form has also been proven.

Keywords: Dirichlet $L-$function, Dirichlet character, prime numbers, basic intervals, additional intervals, estimate, equation, solvability, non-trivial zeros, exceptional zero.

UDC: 511.325

Received: 14.06.2024
Accepted: 24.12.2024

DOI: 10.22405/2226-8383-2024-25-4-5-26



© Steklov Math. Inst. of RAS, 2025