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PRMO 2016 Problem 2 | Number Theory

Try this beautiful interesting problem based on Number Theory from PRMO 2016 Problem 2.

Number Theory Problem: PRMO 2016 Problem 2

The five digit number $2 a 9 b 1$ is a perfect square. Find the value of $a^{b-1}+b^{a-1}$.

Key Concepts

Properties of Perfect Squares

Divisibility Rules of different numbers

Finding the square root of a number

Suggested Book | Source | Answer

Challenge and Thrill of Pre College Mathematics

PRMO 2016

50

Try with Hints

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.

Try this beautiful interesting problem based on Number Theory from PRMO 2016 Problem 2.

Number Theory Problem: PRMO 2016 Problem 2

The five digit number $2 a 9 b 1$ is a perfect square. Find the value of $a^{b-1}+b^{a-1}$.

Key Concepts

Properties of Perfect Squares

Divisibility Rules of different numbers

Finding the square root of a number

Suggested Book | Source | Answer

Challenge and Thrill of Pre College Mathematics

PRMO 2016

50

Try with Hints

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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