2022 SSMO Relay Round 2 Problems/Problem 3

Problem

Let $T =$ TNYWR. Let $a+b = \lfloor \sqrt{T} \rfloor$ . If $a^5 + b^5 = 15$ , then $ab$ has two possible values. The absolute difference of these values is $\frac{x\sqrt{y}}{z}$ , where $x,y$ and $z$ are positive integers, $x$ and $z$ are relatively prime, and $y$ is not divisible by the square of any prime. What is $x+y+z?$

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2022 SSMO Relay Round 2 Problems/Problem 3

Problem

Solution