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Question Number 47186 by naka3546 last updated on 05/Nov/18

$$howtoknowsumofdigits:$$$$3^{313}+3^{354}?$$

Answered by MJS last updated on 06/Nov/18

$${\mathrm{it}}^{\prime }\mathrm{s}‘‘{\mathrm{only}}^{″}\mathrm{a}169-\mathrm{digit}\mathrm{number}$$$$\mathrm{I}\mathrm{squared}\mathrm{mostly}$$$$3^{313}=3^{256}\times 3^{32}\times 3^{16}\times 3^8\times 3$$$$3^{354}=3^{256}\times 3^{64}\times 3^{32}\times 3^2$$$$\mathrm{and}\mathrm{got}$$$$3^{313}+3^{354}=$$$$7960203505214079922814876488736$$$$964293162666208782587346318718$$$$209290966475294261816306379184$$$$210897003690564133950873872361$$$$458647009385180553218054740870$$$$088023659722456492$$$$\Rightarrow \mathrm{sum}\mathrm{of}\mathrm{digits}=765$$

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