# My cryptogram hypothesis

Consider equations, an which ${ A }_{ 1 },{ A }_{ 2 },{ A }_{ 3 },\dots { ,A }_{ n-1 },{ A }_{ n }$ is not necessarily distinct non-zero digits in decimal base and $n, m$ is natural numbers.

1. Prove for $n \ge 5$ that equation below hasn't solution: $\overline { { A }_{ 1 } } +\frac { \overline { { A }_{ 1 }{ A }_{ 2 } } }{ \overline { { A }_{ 2 } } } +\frac { \overline { { A }_{ 1 }{ A }_{ 2 }{ A }_{ 3 } } }{ \overline { { A }_{ 2 }{ A }_{ 3 } } } +\dots +\frac { \overline { { A }_{ 1 }{ A }_{ 2 }{ A }_{ 3 }\dots { A }_{ n-1 }{ A }_{ n } } }{ \overline { { A }_{ 2 }{ A }_{ 3 }\dots { A }_{ n-1 }{ A }_{ n } } } =m$

2. Prove for $n \ge 4$ that equation below hasn't solution: $\overline { { A }_{ 1 } } +\frac { \overline { { A }_{ 1 }{ A }_{ 2 }{ A }_{ 1 } } }{ \overline { { A }_{ 2 } } } +\frac { \overline { { { A }_{ 1 }{ A }_{ 2 }{ A }_{ 3 }{ A }_{ 2 }{ A }_{ 1 } } } }{ \overline { { { A }_{ 2 }{ A }_{ 3 }{ A }_{ 2 } } } } +\dots +\frac { \overline { { { A }_{ 1 }{ A }_{ 2 }\dots { A }_{ n-1 }{ A }_{ n }{ A }_{ n-1 }\dots { A }_{ 2 }{ A }_{ 1 } } } }{ \overline { { A }_{ 2 }\dots { A }_{ n-1 }{ A }_{ n }{ A }_{ n-1 }\dots { A }_{ 2 } } } =m$ Note by Ilya Pavlyuchenko
5 months, 3 weeks ago

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Thank you, it is interesting

- 5 months, 1 week ago

Isn't A(1)=1 and A(2)=2 and A(i)=0 for all i>2 a solution for equation 1?

- 5 months ago

Whoops, just saw the requirement for non-zero digits.

- 5 months ago

@Yajat Shamji, thank you for reporting the spam user. In the future, please tag my account so we can take care of the offending account as soon as possible.

Staff - 5 months ago

@Ilya Pavlyuchenko, I don't know how to write cryptograms - I have got one for a problem but I can't write it. Can you give me any help on how to write cryptograms?

- 5 months, 2 weeks ago

For working in $\LaTeX$ use plugin on browser Daum Equation Editor. You can download it free in Google Chrome Shop.

- 5 months, 2 weeks ago

Thanks for the alternative!

- 5 months, 1 week ago

No problem!

- 5 months, 1 week ago

@Brilliant Mathematics, I have noticed that in all the profiles of the spam users, the country they come from is Pakistan. Something relevant at all?

No, I do not think so. But thanks for notifying us!

Staff - 5 months ago