performance tuning – Solving a diophantine equation in ‘large’ values

Let’s first discuss what I am trying to solve: I want to solve the diophantine equation stated below for relatively ‘large’ values of $r$.

$$frac{a(a + 3)(a(r – 9) + (7 – r))}{12}=frac{b (3 + b (-5 + r) – r)}{7}tag1$$

The question I have is: how can I solve this equation, in the positive integers, for large values of $r$?


My try, I wrote the following code:

In(1):=Solve({(a*(a + 3)*(a*(r - 9) + (7 - r)))/
    12 == (b*(3 + b*(-5 + r) - r))/7, 10^5 <= r <= 10^5 + 1000}, {r, a, 
  b}, PositiveIntegers)

The only thing I got are ConditionalExpression which I am not looking for, so how can I solve this?