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Question Number 177000 by Ar Brandon last updated on 29/Sep/22

$$\mathrm{Let}a\mathrm{and}b\mathrm{be}\mathrm{positive}\mathrm{integers}.$$$$\mathrm{If}118!+119!=5^{a}b\mathrm{then}\mathrm{what}\mathrm{is}{a}_{\max }?$$

Answered by BaliramKumar last updated on 29/Sep/22

$$118!+119!=118!(1+119)=120\times 118!$$$$5^1\times 24\times 118!\begin{array}{|cc|}\hline 5& 118\\ 5& 23\\ 5& 4\\ & 0\\ \hline\end{array}$$$$a_{max}=1+23+4+0=28$$

Commented by Ar Brandon last updated on 29/Sep/22

Thanks! I now understand your method. I didn't get it at first.

Commented by Tawa11 last updated on 02/Oct/22

$$\mathrm{Great}\mathrm{sir}$$

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