What is the integer solution to 42 = x^3 + y^3 + z^3 ?

Question

Puzzling · Accepted Answer

Regarding:
x³ + y³ + z³ = n

In 2016, all of the numbers less than 100 that were not 4 or 5 mod 9 had solutions, apart from 33 and 42.

Just recently a solution was found for n=33 by a number theorist in the UK, Andrew Booker.

8,866,128,975,287,528³ + (-8,778,405,442,862,239)³ + (-2,736,111,468,807,040)³ = 33

It had been conjectured, in 1992, that every n that was not equal to 4 or 5 mod 9 had infinitely many solutions but this is still an open question.

As if this writing, a solution hasn't been found for 42, but again, according to the conjecture, there isn't just *the* solution, but infinitely many integer solutions.

? · Answer

42 = x^3 + y^3 + z^3 
No integer solution

Jeff Aaron · Answer

No integer solution.

What is the integer solution to 42 = x^3 + y^3 + z^3 ?

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