Bremner-Macleod numbers

are smallest positive integer solution \((a,b,c)\) of the following : $$\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}=N$$ where \(N\) is a positive integer.

The equation and the sizes of its solutions were discussed by Andrew Bremner and Allan Macleod. For all odd \(N\) and some even \(N\), the equation has no positive integer solutions. For \(N\le200\), the most digits in \(a,b,c\) of the are shown below: For \(N=896\), \(a\) has more than 2.187 trillion digits.