Is 404 in base -31 a palindrome?

Number Theory Level pending

If you visit a broken link on Brilliant like https://brilliant.org/urldoesntexist you get interesting facts about 404. One of them says 404 in base -31 is a palindrome.

So figure out what is 404 in base -31.


The answer is 1181.

Gokul Nk by Gokul Nk , 34, India

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1 solution

Sachin Sharma
Dec 30, 2015

We have 404 = 1 ( − 31 ) 2 + 18 ( − 31 ) 1 + 1 ( − 31 ) 0 404 = 1(-31)^2+18(-31)^1+1(-31)^0

Thus ( 404 ) 10 = ( 1181 ) − 31 (404)_{10} = (1181)_{-31}

But not sure about how 1181 1181 would be a palindrome

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