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October 19, 2026The Mathematical Gazette

Solution to p ( x ) 2 = 1 + p ( x − 1) p ( x + 1)

S. C. Dutta Roy

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Abstract

In [1], De and Bhattacharya conclude their article with the following problem for the reader:Determine all polynomials p with real coefficients that satisfy (1) p(x)2=1+p(x−1)p(x+1) for all real x....

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S. C. Dutta Roy (2026) studied this question.

synapsesocial.com/papers/6ad855c9c31ae80836fdb4a7 https://doi.org/10.1080/00255572.2026.2745722

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Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1On the Lebesgue-Nagell equation $x^2-2 = y^p$2025
2On the Diophantine Equation p^x+(p+1)^y=z^2, where p is Prime2024
3On the Diophantine equation $4(7^x)-p^y=z^2$2025
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5Solution of the Diophantine equation $x^2 + p^k=y^n$2024

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