Maths in Europe: The ultimate question

If you are a reader of the Hitchhiker's guide to the galaxy, you probably know that 42 is the answer to the Ultimate Question of Life, the Universe, and Everything. The choice of the number by Douglas Adams was quite random, excluding the simple fact that the number liked the writer. Yet the 42 was the protagonist of a recent news related to one of the open problems of mathematics:
Is there a number that is not 4 or 5 modulo 9 and that cannot be expressed as a sum of three cubes?
To find an answer to this question, mathematicians used numerical methods. In particular, Andreas-Stephan Elsenhans and Jorg Jahnel using a particular vector space, searched solutions of the following diophantine equation:
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