SOLUTION: If A power of B + B to the power of A = 2044, wht are the values of A and B?

Question 8031: If A power of B + B to the power of A = 2044, wht are the values of A and B?
Answer by khwang(438) (Show Source): You can put this solution on YOUR website!
If A^B + B^A = 2044 (You should type in math notation, not in English!!!)
then A, B are both even or odd.
If A,B are >= 2, try 3^7+7^3 = 2530 > 2044,
2^10+10^2 = 1124,
or 3^5 + 5^3 ... (only limited choices and all fail)
As the table below:

A B A^B +B^A
---------------------------
2 10 1124
3 5 368
3 7 2530
4 4 512
4 6 5392

Hence, one of them is 1 and so another is 2043 as a trivial solution.

In fact, 1^(n-1) + (n-1)^1 = n for any positive integer n.
Thus this question somehow does not make any sense in math, because
there is no any relation hiding inside A^B +B^A.

Kenny

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