Try this beautiful interesting problem based on Number Theory from PRMO 2016 Problem 2.
The five digit number $2 a 9 b 1$ is a perfect square. Find the value of $a^{b-1}+b^{a-1}$.
Properties of Perfect Squares
Divisibility Rules of different numbers
Finding the square root of a number
Challenge and Thrill of Pre College Mathematics
PRMO 2016
50
An odd perfect square is of the form $8k+1$
Hence $8| 2a9b0$
Hence $8 | 2a000 + 9b0 $
$8 | 900 +b0 $
$ 8 | b4$
Therefore the possible values of b are $6,2$
So possible numbers are $2a921,2a961$
Now check for the possible values of $a$ and calculate the square root to check if it is a perfect square
The only valid solution is $a=5$
Hence calculate the required expression.
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