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Question Number 106422 by Algoritm last updated on 05/Aug/20

Commented by mr W last updated on 05/Aug/20

$$73!=1\times 2\times 3\times ...\times 49\times 50\times ...\times 73$$$$73!=0\left(mod2\right)$$$$73!=0\left(mod3\right)$$$$73!=0\left(mod4\right)$$$$...$$$$73!=0\left(mod49\right)$$$$73!=0\left(mod50\right)$$$$...$$$$73!=0\left(mod73\right)$$

Answered by Olaf last updated on 24/Sep/20

$$73!=48!\times 49\times \frac{73!}{49!}$$$$73!=49k\mathrm{with}k=\frac{73!}{49}$$$$\Rightarrow 73!\equiv 0\left[49\right]$$

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