Determine all possible triplets (A,B,C) of positive integers with A ≤ B ≤ C that satisfy this system of equations:
A = P(B)+ P(C), B = P(A) + P(C), and C = P(A) + P(B)
Prove that there are no others.
|No Solution Yet||Submitted by K Sengupta|
|re(3): results so far, but no proof in sight||
I've managed to establish an upper bound for C as follows:
let C have n digits. Then A,B can have at most n digits. Thus P(A) and P(B) can be at most 9^n each. Thus
P(A)+P(B)<=2*9^n. However, for C to have n digits, we require
Unfortunately this upper limit does not lend itself to a timely exhaustive search. However, I have a feeling that there is more clever methods which would allow for a much smaller upper limit and thus permitting an exhaustive search.
|Posted by Daniel on 2013-08-04 15:42:58|