<s>[INST] the diophantine forms of the equation $a^2 +b^3 = c^5$ I just want to know the forms of the numbers a,b and c in the Diophantine equation:
               $a^2 +b^3 = c^5$
 [/INST] See OEIS sequence A178130
$$\eqalign{104^2 + 28^3 &= 8^5\cr
654^2 + 127^3 &= 19^5\cr
2816^2 + 32^3 &= 24^5\cr
3912^2 + 124^3 &= 28^5\cr
4096^2 + 256^3 &= 32^5\cr
6048^2 + 288^3 &= 36^5\cr
48500^2 + 275^3 &= 75^5\cr
19683^2 + 1458^3 &= 81^5\cr
65216^2 + 1008^3 &= 88^5\cr
77824^2 + 1280^3 &= 96^5\cr
\ldots}$$
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