S. Panda

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20122026

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math.NT2026

Euler characteristic of the Selmer group attached to an Artin representation

Subhasis Panda

Longo and Vigni extended a result of Greenberg by giving a relation between the cardinality of the Selmer group and the characteristic power series of its Pontryagin dual over the…

math.NT2026

On the Diophantine Equation $p^{x} + (2 p + 1)^{y} = z^{2}$ with Consecutive Exponents

Subhasis Panda

We study the Diophantine equation $p^{x} + (2 p + 1)^{y} = z^{2}$ over positive integers $x$ , $y$ and $z$ for every odd prime $p$ . We prove that $(x, y, z) = (2, 1, p + 1)$ is the unique solution exc…

Euler characteristic of the Selmer group attached to an Artin representation

On the Diophantine Equation px+(2p+1)y=z2 with Consecutive Exponents

On the Diophantine Equation $p^{x} + (2 p + 1)^{y} = z^{2}$ with Consecutive Exponents