Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Is there a non-square positive integer $n$, that $\sqrt{n}$ has only even digits in its decimal representation ?

share|improve this question
5  
It's believed not: every irrational algebraic number is conjectured to be normal (and hence its decimal expansion contains all $10$ digits). I don't know if this special case has been solved. –  Chris Eagle Dec 13 '12 at 18:58
    
Out of pure interest, does "normal" mean that every digit appears equally "often"? –  CBenni Dec 13 '12 at 19:26
    
I think for this special case, calculate the probability that a real number has decimal expression with only even digits might be helpful. –  ougao Dec 13 '12 at 19:27
3  
normal number en.wikipedia.org/wiki/Normal_number –  ougao Dec 13 '12 at 19:28
1  
@ougao: How will that help? –  Chris Eagle Dec 13 '12 at 19:35

1 Answer 1

No such $n$ is known.

If one were found, it would be the biggest shock in Mathematics since, well, maybe since ever; certainly, since Godel's incompleteness results.

No proof is known that such an $n$ does not exist.

share|improve this answer
    
Could you elaborate the connection of this question with Godel's Theorem? Thanks :) –  Mahan Dec 14 '12 at 6:34
1  
The only connection is that Godel's results came as a shock, and finding such an $n$ would be at least as big a shock. The connection is sociological, not mathematical. –  Gerry Myerson Dec 14 '12 at 11:58

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.