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A diophantine equation involving special prime numbers

Stoyan Dimitrov — 2023

Czechoslovak Mathematical Journal

Let [ · ] be the floor function. In this paper, we prove by asymptotic formula that when 1 < c < 3441 2539 , then every sufficiently large positive integer N can be represented in the form N = [ p 1 c ] + [ p 2 c ] + [ p 3 c ] + [ p 4 c ] + [ p 5 c ] , where p 1 , p 2 , p 3 , p 4 , p 5 are primes such that p 1 = x 2 + y 2 + 1 .

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