Determine all possible values of a duodecimal (base 12) positive integer N, such that N is obtained by adding the squares of its digits.
Bonus Question:
Determine all possible values of a octodecimal (base 18) positive integer N, such that N is obtained by adding the squares of its digits.
General formula: a(a1)+b(b12)+c(c12^2).... = 0, but since all variables are integers between 0 and 11, c and all following terms must be zero.
Then the solutions are:

1;

25(12)=29=2^2+5^2;

A5(12)=125=100+25.
Bonus question: Similarly, the solutions are:
 1;
 48(18)=80=8^2+4^2;
 E8(18)=260=14^2+8^2;
 69(18)=117=6^2+9^2;
 C9(18)=225=12^2+9^2.
Edited on October 17, 2010, 3:22 am

Posted by broll
on 20101016 15:58:39 