P1400 [CERC2016] Easy Equation

Given an integer $k$ greater than $1$, it is possible to prove that there are infinitely many triples of positive integers $(a, b, c)$ that satisfy the following equation: $$a^2+b^2+c^2=k(ab+bc+ca)+1$$ Given positive integers $n$ and $k$, find $n$ arbitrary triples $(a_1, b_1, c_1), (a_2, b_2, c_2), \cdots , (a_n, b_n, c_n)$ that all satisfy the equation. Furthermore, all $3n$ integers $(a_1, b_1, c_1), (a_2, b_2, c_2), \cdots , (a_n, b_n, c_n)$ should be different positive integers with at most $100$ decimal digits each.

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