Find all numbers N = a₁a₂a₃...a_n greater than 1, with no leading zeros, no zeros, which fits this equation:

N = a₁^a₁ + a₂^a₂ + a₃^a₃ + ... + a_n^a_n

Clarifying, N = 23 doesn´t work because 2² + 3³ is equal to 31, not 23.

(In reply to Second Computer Solution by brianjn)

 

If you research the definition of 0^0 you will find  that it should be set according to the needs of a specific problem.

Depending on the context where 0^0 occurs, you might wish to substitute it with 1, indeterminate or undefined/nonexistent 

One might say that  a^0 is 1 for any a , the other will claim that  0^a is zero for any a ,      but  if we  consider functions f(x) and g(x) then the limit of f^g when x ==>0 may be any number between 0 and 1; e.g. lim (e^(-1/x))^x equals 1/e if x ==>0.

Since our problem specifies "no zeros" I see no reason  to introduce an irrelevant definition of 0^0=0.

Please try Google (several entries) for
Zero to the zero power

Posted by Ady TZIDON on 2008-11-15 23:37:51