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Find all integers n for which the equation $$x^3+y^3+z^3-3xyz=n$$ is solvable in positive integers.

Yooooooooooo
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  • What did you try? – pyridoxal_trigeminus Aug 11 '22 at 04:58
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    first strategy is to factorise both sides.LHS is $(x + y + z) (x^2 + y^2 + z^2-xy-yz-zx)$. For RHS if $n$ is prime then it's the simplest case as one of the factors on LHS would be one . And in case n is productc of two pimes then also wecan say one of factors on LHS is equalto one of those primes. Things get more complicated as nos of factors in $n$ increases. – ishandutta2007 Aug 11 '22 at 05:05
  • Try factorising the LHS. – Hersh Aug 11 '22 at 05:08

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