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Question: Find all positive integers $k$ for which the equation

Question:Find all positive integers $k$ for which the equation

vanish 0 Maple
diophantine_equation
1 hour ago
0

a2+b2+c2+1=k abca^2+b^2+c^2+1 = k\,abca2+b2+c2+1=kabc

has a solution in positive integers $a,b,c$. For that $k$, prove every solution has $a,b,c$ all odd, and that every solution can be reduced to $(1,1,1)$ by repeated moves $(a,b,c)\mapsto(a,b,4ab-c)$.
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