Displaying similar documents to “On the Diophantine equation x 2 + 2 α 5 β 17 γ = y n

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).

A note on the number of S -Diophantine quadruples

Florian Luca, Volker Ziegler (2014)

Communications in Mathematics

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Let ( a 1 , , a m ) be an m -tuple of positive, pairwise distinct integers. If for all 1 i < j m the prime divisors of a i a j + 1 come from the same fixed set S , then we call the m -tuple S -Diophantine. In this note we estimate the number of S -Diophantine quadruples in terms of | S | = r .

Method of infinite ascent applied on - ( 2 p · A 6 ) + B 3 = C 2

Susil Kumar Jena (2013)

Communications in Mathematics

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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 · A 6 ) + B 3 = C 2 for any positive integral values of p when p 1 (mod 6) or p 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.