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MathNet 2006 — Part 03 Question 163

Math Olympiad Vault · MathNet 2006 — Part 03

Question 163

For every positive integer $n$, let us use non-negative integers $a, b, c, d, e, f, g, h$

$$
n=\frac{2^{a}-2^{b}}{2^{c}-2^{d}} \cdot \frac{2^{e}-2^{f}}{2^{g}-2^{h}}
$$

find? The answer must be justified.