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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

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

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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

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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