Determine all possible pairs (A,B) of positive integers that satisfy this equation:
Provide valid reasoning for your answer.
Notes:
(i) x^x^x is equal to x^(x^x) and NOT (x^x)^x.
(ii) Computer program/excel solver assisted solutions are welcome, but a semi-analytic (hand calculator and p&p) methodology is preferred.
(iii) Adapted from a problem appearing in Taiwan M.O: 2000.
clearvars,clc
for tot=sym(2):200
for a=sym(1):tot-1
b=tot-a;
if b^(a^2)==a^(b+2)
disp([a b b^(a^2) a^(b+2)])
end
end
end
finds only
[a, b, b^(a^2), a^(b+2)]
[1, 1, 1, 1]
[2, 2, 16, 16]
|
|
Posted by Charlie
on 2023-08-18 08:58:10 |
computer findings
