Arithmetic Operation

Algebra Level 4

Consider the arithmetic operations \blacktriangle and \blacktriangledown defined by

ab={a if abb if a<bab={a if abb if a>b\large \begin{aligned} a \blacktriangle b & = \begin{cases} a & \text{ if } \lvert a \rvert \geq \lvert b \rvert \\ b & \text{ if } \lvert a \rvert < \lvert b \rvert \end{cases} \\ a\blacktriangledown b & = \begin{cases} a & \text{ if } \lvert a \rvert \leq \lvert b \rvert \\ b & \text{ if } \lvert a \rvert > \lvert b \rvert \end{cases} \end{aligned}

How many integers kk are there such that (209)(k5)=5?(-20 \blacktriangle 9) \blacktriangledown (k \blacktriangle 5)=5?

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