By six

From the digits 1,2,3,4 we create the long integer number 123412341234. .. .. , which will have 962 digits. Is this number divisible by 6?

Result

x=

Yes

No

Step-by-step explanation:

$$\begin{gathered} n=962 \\ {n}_1=n\mathrm{/}4=962\mathrm{/}4={\displaystyle \frac{481}{2}}=240\frac{1}{2}=240.5 \\ {n}_2=\lfloor n_1\rfloor =\lfloor 240.5\rfloor =240 \\ {n}_3=n-4\cdot n_2=962-4\cdot 240=2 \\ s=n_2\cdot (1+2+3+4)+1+2=240\cdot (1+2+3+4)+1+2=2403 \\ {s}_3=s\mathrm{/}3=2403\mathrm{/}3=801 \\ 12341234\dots 123412 \\ x=1=1 \end{gathered}$$

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