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Keywords:
higher order Diophantine equations; method of infinite ascent; Diophantine equation $-(2^p\cdot A^6) + B^3 = C^2$
higher order Diophantine equations; method of infinite ascent; Diophantine equation $-(2^p\cdot A^6) + B^3 = C^2$
Summary:
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 $-(2^p\cdot A^6) + B^3 = C^2$ for any positive integral values of $p$ when $p \equiv 1$ (mod 6) or $p \equiv 2$ (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.
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