Can you think of an elegant proof for this one?

Number Theory Level pending

How many pairs of the positive integers ( a , b ) (a, b) satisfy the following equation ( 15 a + b ) ( 15 b + a ) = 3 k , k Z (15a+b)\cdot (15b+a)=3^k, k \in \mathbb{Z}

None Depends on k k Infinitely many

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