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Number TheoryEasyHard Number Theory

Hard Number Theory · Easy problem

Use Legendre's formula ⌊n7⌋+⌊n49⌋+⋯\left\lfloor \dfrac{n}{7} \right\rfloor + \left\lfloor \dfrac{n}{49} \right\rfloor + \cdots to find the largest kk such that 7k7^k divides 100!100!.