Inductive case: Fix an arbitrary \(n\ge 2\) and assume \(P(k)\) is true for all \(k \lt n\text{.}\) Consider a \(n\)-square rectangular chocolate bar. Break the bar once along any row or column. This results in two chocolate bars, say of sizes \(a\) and \(b\text{.}\) That is, we have an \(a\)-square rectangular chocolate bar, a \(b\)-square rectangular chocolate bar, and \(a+b = n\text{.}\)
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