Displaying similar documents to “On the diophantine equation x 2 + 5 k 17 l = y n ”

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.

On the Diophantine equation x 2 + 2 α 5 β 17 γ = y n

Hemar Godinho, Diego Marques, Alain Togbé (2012)

Communications in Mathematics

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In this paper, we find all solutions of the Diophantine equation x 2 + 2 α 5 β 17 γ = y n in positive integers x , y ≥ 1 , α , β , γ , n ≥ 3 with gcd ( x , y ) = 1 .