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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.

Math Olympiad Program

Subscribe to Cheenta at Youtube


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.

Math Olympiad Program

Subscribe to Cheenta at Youtube


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