Discussion: This student solves a problem very similar to an earlier one by the same method: An initial solution is found, (a,b,c). Then a and b are put in the equation for x and y which results in an integral monic equation in z which has an integer solution and so there must be a second integer solution. In this way each solution gives rise to a second whose values get progressively larger and therefore one has an algorithm for generating infinitely many solutions.

Written response: You have clearly become an expert at this type of problem. You might try the same approach to the problem dealing with an urn with black and white balls with a proscribed probability of picking one black and one white ball when they are removed without replacement.

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