Solution to Problem 2

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Correct Answer:

\(p = 3, q=2\) and \(r=2\) is the only solution.

Correct answers were given by Manjunath M. R. (Infosys), Harshitha K. N. (Reserahc scholar, UOM) and Nagendra P (Research Scholar, UOM). But coomplete valid justifications were given by Harshitha K. N. and Manjunath M. R.

Solution.

From the given information, we infer that

\(2(3r-p) = 3q\).

Since 2 is a prime and as it divides \(3q\), it must divide 3 or \(q\). Since 2 does not divide 3, it must divide \(q\). Since \(q\) is also prime, we must have \(q=2\). Similarly we can show that \(p = 3\). Hence \(6r = 6+6=12\) implying \(r=2\).