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Question Number 193286 by BaliramKumar last updated on 09/Jun/23

$$\mathrm{Let}{}^{\prime }{\mathrm{P}}^{\prime }\mathrm{is}\mathrm{a}\mathrm{prime}\mathrm{number}(\mathrm{P}>1000).$$$$\mathrm{If}{}^{\prime }{\mathrm{P}}^{\prime }\mathrm{devided}\mathrm{by}1000,\mathrm{then}\mathrm{remainder}\mathrm{is}{}^{\prime }{\mathrm{r}}^{\prime }.$$$$\mathrm{How}\mathrm{many}\mathrm{value}\mathrm{of}{}^{\prime }{\mathrm{r}}^{\prime }?$$

Commented by Tinku Tara last updated on 09/Jun/23

$$\mathrm{All}\mathrm{number}\mathrm{other}\mathrm{than}\mathrm{multiple}$$$$\mathrm{of}2\mathrm{and}5\mathrm{are}\mathrm{possible}.$$

Commented by BaliramKumar last updated on 09/Jun/23

$$\mathrm{yes},\mathrm{but}\mathrm{total}\mathrm{value}\mathrm{of}\mathbf{r}=?$$

Answered by BaliramKumar last updated on 09/Jun/23

$$\mathbf{\Phi }\left(1000\right)=\mathbf{\Phi }\left({10}^3\right)=4\times {10}^{3-1}=4\times {10}^2=400$$

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