Displaying similar documents to “On the diophantine equation xp - x = yq - y.”

On two-parametric family of quartic Thue equations

Borka Jadrijević (2005)

Journal de Théorie des Nombres de Bordeaux

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We show that for all integers m and n there are no non-trivial solutions of Thue equation x 4 - 2 m n x 3 y + 2 m 2 - n 2 + 1 x 2 y 2 + 2 m n x y 3 + y 4 = 1 , satisfying the additional condition gcd ( x y , m n ) = 1 .

On the diophantine equation x 2 + 5 k 17 l = y n

István Pink, Zsolt Rábai (2011)

Communications in Mathematics

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Consider the equation in the title in unknown integers ( x , y , k , l , n ) with x 1 , y > 1 , n 3 , k 0 , l 0 and gcd ( x , y ) = 1 . Under the above conditions we give all solutions of the title equation (see Theorem 1).