On the solutions of certain Lebesgue-Ramanujan-Nagell equations

2020/11/02 by Chakraborty, Kalyan, Hoque, Azizul, Sharma, Richa
#11D41 #11D61 #11R29 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2011.01099

Abstract

We completely solve the Diophantine equation x²+2^k11^ℓ19^m=yⁿ in integers x,y≥ 1;~ k,ℓ, m≥ 0~ and n≥ 3 with gcd(x,y)=1, except the case 2| k, 2\nmid ℓ m and 5| n. We use this result to recover some earlier results in the same direction.

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