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# Largest Possible Value | PRMO-2019 | Problem 17 Try this beautiful problem from PRMO, 2019 based on Largest Possible Value.

## Largest Possible Value | PRMO | Problem-17

Let a, b, c be distinct positive integers such that , and are all perfect squares.
What is the largest possible value of smaller than ?

• • • ### Key Concepts

Number theory

Perfect square

Integer

Answer: PRMO-2019, Problem 17

Pre College Mathematics

## Try with Hints

Let … (i) … (ii) … (iii)

Now since , , are distinct positive integers,
Therefore, , , will also be positive integers, Now, we need to find largest value of less than Now, to get a, b, c all integers , , all must be of same parity, i.e. either all three are even or all three
are odd.

Can you now finish the problem ..........

Let us maximize , for both cases.
If , , are all even.
Therefore,   Which on solving, give , , and If x, y, z are all odd   Which on solving, give , , and Can you finish the problem........

Therefore Maximum value of ## Subscribe to Cheenta at Youtube

Try this beautiful problem from PRMO, 2019 based on Largest Possible Value.

## Largest Possible Value | PRMO | Problem-17

Let a, b, c be distinct positive integers such that , and are all perfect squares.
What is the largest possible value of smaller than ?

• • • ### Key Concepts

Number theory

Perfect square

Integer

Answer: PRMO-2019, Problem 17

Pre College Mathematics

## Try with Hints

Let … (i) … (ii) … (iii)

Now since , , are distinct positive integers,
Therefore, , , will also be positive integers, Now, we need to find largest value of less than Now, to get a, b, c all integers , , all must be of same parity, i.e. either all three are even or all three
are odd.

Can you now finish the problem ..........

Let us maximize , for both cases.
If , , are all even.
Therefore,   Which on solving, give , , and If x, y, z are all odd   Which on solving, give , , and Can you finish the problem........

Therefore Maximum value of ## Subscribe to Cheenta at Youtube

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