On the Diophantine equation $X^2 - (2^{2m}+1)Y^4 = -2^{2m}$

Michael Stoll; P. G. Walsh; Pingzhi Yuan

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Hui Lin Zhu (2011)

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Mihai Cipu, Tim Trudgian (2016)

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We consider Diophantine quintuples a, b, c, d, e. These are sets of positive integers, the product of any two elements of which is one less than a perfect square. It is conjectured that there are no Diophantine quintuples; we improve on current estimates to show that there are at most $5.441 \cdot 10^{26}$ Diophantine quintuples.

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On the Diophantine equation $x ² + 2^{α} 13^{β} = y ⁿ$

Florian Luca, Alain Togbé (2009)

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The Diophantine equation ${(b n)}^{x} + {(2 n)}^{y} = {((b + 2) n)}^{z}$

Min Tang, Quan-Hui Yang (2013)

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Recently, Miyazaki and Togbé proved that for any fixed odd integer b ≥ 5 with b ≠ 89, the Diophantine equation $b^{x} + 2^{y} = {(b + 2)}^{z}$ has only the solution (x,y,z) = (1,1,1). We give an extension of this result.

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A note on the Diophantine equation P(z) = n! + m!

Maciej Gawron (2013)

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We consider the Brocard-Ramanujan type Diophantine equation P(z) = n! + m!, where P is a polynomial with rational coefficients. We show that the ABC Conjecture implies that this equation has only finitely many integer solutions when d ≥ 2 and $P (z) = a_{d} z^{d} + a_{d - 3} z^{d - 3} + \dots + a ₁ x + a ₀$ .

On the Diophantine equation $(\binom{n}{k_{1}, . . ., k_{s}}) = x^{l}$

Peng Yang, Tianxin Cai (2012)

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Samir Siksek, John E. Cremona (2003)

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Maohua Le (2003)

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Method of infinite ascent applied on $- (2^{p} \cdot A^{6}) + B^{3} = C^{2}$

Susil Kumar Jena (2013)

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In this paper, the author shows a technique of generating an infinite number of coprime integral solutions for $(A, B, C)$ of the Diophantine equation $- (2^{p} \cdot A^{6}) + B^{3} = C^{2}$ for any positive integral values of $p$ when $p \equiv 1$ (mod 6) or $p \equiv 2$ (mod 6). For doing this, we will be using a published result of this author in The Mathematics Student, a periodical of the Indian Mathematical Society.

Displaying similar documents to “On the Diophantine equation X 2 - ( 2 2 m + 1 ) Y 4 = - 2 2 m ”

Displaying similar documents to “On the Diophantine equation $X^{2} - (2^{2 m} + 1) Y^{4} = - 2^{2 m}$ ”