# Two Looming Towers Of Powers

Number Theory Level 5

Let $$a_{n+1} = 2^{a_n}$$ and $$b_{n+1} = 3^{b_n}$$ both for $$n \ge 1.$$

If $$a_1 = 2$$ and $$b_1 = 3$$, then find $\min_{x\ge 2, y \ge 2} |a_x-b_y|.$

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