Munchausen Number

A Munchausen Number is a number that is equal to the sum of its digits each raised to a power equal to that digit. It is also called perfect digit-to-digit invariant (PDDI) because of its feature.1 is a Munchausen number. If we consider 0^0 as 0 there is a Munchausen number 438579088. But as 0 is undefined we can't consider this number. There is another Munchausen number besides 1. What is that?

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
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Comments

3435 learned it from Numberphile.

Bob Krueger - 8 years, 1 month ago

3435

Tan Li Xuan - 8 years, 1 month ago

exactly wolfram mathworld says there are four munchausen number....they are 0,1,3435,and 438579088.......If the definition (0^(0))=0 is adopted.....

Sayan Chaudhuri - 8 years, 1 month ago

$0^0$ is undefined, remember? Discussion

Aditya Parson - 8 years, 1 month ago

but wolfram says if and only if (iff) it(i.e. 0^(0) ) is defined only then the number could be adopted as munchausen number...... i have gone through the discussion ,you mentioned,before many times ....thanxx....but see here....find the statement that i gave is in the last line.....hope you understand my source.....

Sayan Chaudhuri - 8 years, 1 month ago

yes but I previously mentioned we can't take it as 0^0 is undefined

jawwad shadman siddique - 8 years, 1 month ago

can anyone give me an exact proof with logical reasoning how 0^0 is undefined?

jawwad shadman siddique - 8 years, 1 month ago

3435 damn sure

Shourya Pandey - 8 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$