Problems

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Found: 2

Let us introduce the notation – we denote the product of all natural numbers from 1 to \(n\) by \(n!\). For example, \(5!=1\times2\times3\times4\times5=120\).

a) Prove that the product of any three consecutive natural numbers is divisible by \(3!=6\).

b) What about the product of any four consecutive natural numbers? Is it always divisible by 4!=24?