Question 35
A triple of integers $(a, b, c)$ is called *artistic* if the number $\frac{ab+bc+ca}{a+b+c}$ is also an integer.
a) Determine the integers $n$ for which the triples $(n, n+1, n+3)$ are artistic.
b) If $(x, y, z)$ is an artistic triplet, prove that $\frac{x^4+y^4+z^4}{x+y+z}$ is an integer.
a) Determine the integers $n$ for which the triples $(n, n+1, n+3)$ are artistic.
b) If $(x, y, z)$ is an artistic triplet, prove that $\frac{x^4+y^4+z^4}{x+y+z}$ is an integer.