New solutions are found for a Diophantine equation involving prime numbers, suggesting limitations on certain primes.
In this paper, we present new series of solutions of the Diophantine equation 3x + p5y = z2 where p is a prime number and x; y and z are nonnegative integers using elementary techniques. Moreover, the equation has no solution if p is equivalent to 5 or 7 modulo 24.
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Laipaporn et al. (2019) studied this question.
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