In 1971 the proof below was given that has no integer solutions, using some difficult computations in the field .
In 1973 it was observed that the equation reduces to mod 9, which has no solutions.
Finkelstein, R., & London, H. (1971). On D. J. Lewis’s Equation x^3 + 117y^3 = 5. Canadian Mathematical Bulletin, 14(1), 111-111. doi:10.4153/CMB-1971-020-x
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