On the diophantine equation 
                
                  
                
                $$\varvec{y^{2} = \prod _{i \le 8}(x + k_i)}$$
                
                  
                    
                      
                        y
                        2
                      
                      =
                      
                        ∏
                        
                          i
                          ≤
                          8

Ryali, Srikanth; Subburam, S.

doi:10.1007/s12044-018-0416-1

Cited by 2 publications

(2 citation statements)

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“…Lemma 4 (Srikanth and Subburam [13]). Let p be a prime number, B(x) and C(x) be nonzero rational polynomials with deg(C(x)) < (p − 1) deg(B(x)), l be a positive integer such that lB(x) and l p C(x) have integer coefficients for any nonnegative integer i and δ ∈ {1, −1}:…”

Section: Proofsmentioning

confidence: 99%

“…where c 2 can be bounded using the linear form of the logarithmic method in Laurent, Mignotte, and Nesterenko [12], and an immediate estimation is The result of Hajdu, Laishram, and Tengely in [5] is much stronger than the following corollary. They explicitly obtained all solutions for the values k ≤ 10 using the MAGMA computer program along with two well-known methods (See Subburam [6], Srikanth and Subburam [13], and Subburam and Togbe [14]), after proving that n ≤ 19,736 for 1 ≤ k ≤ 10. Here, we have Corollary 1.…”

Section: Introductionmentioning

confidence: 99%

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On the Ternary Exponential Diophantine Equation Equating a Perfect Power and Sum of Products of Consecutive Integers

et al. 2021

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Consider the Diophantine equation yn=x+x(x+1)+⋯+x(x+1)⋯(x+k), where x, y, n, and k are integers. In 2016, a research article, entitled – ’power values of sums of products of consecutive integers’, primarily proved the inequality n= 19,736 to obtain all solutions (x,y,n) of the equation for the fixed positive integers k≤10. In this paper, we improve the bound as n≤ 10,000 for the same case k≤10, and for any fixed general positive integer k, we give an upper bound depending only on k for n.

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Section: Proofsmentioning

confidence: 99%