On the Diophantine equation f(x)=2f(y)

2018/10/16 by Sanjay Bhatter, Richa Sharma, Bhatter, Sanjay +1
Computer Science · Mathematics · #11D41 #11D45 #11D61 #Algebraic Geometry and Number Theory #Chaos-based Image/Signal Encryption #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1810.06817

openalex publication_date 2018/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f(x)=x²(x²-1)(x²-2)(x²-3). We prove that the Diophantine equation f(x)=2f(y) has no solutions in positive integers x and y, except (x, y)=(1, 1).

Related

• The diophantine equation (2^k-1)(3^k-1)=xⁿ
• Diophantine equations involving Euler function
• On the Diophantine equation F_n-F_m=2^a
• Diophantine approximation and the equation (a² c x^k - 1)(b² c y^k - 1) = (abc z^k - 1)²
• Diophantine equations in two variables