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# Ordered Pairs | PRMO-2019 | Problem 18

Try this beautiful problem from PRMO, 2019, Problem 18 based on Ordered Pairs.

## Orderd Pairs | PRMO | Problem-18

How many ordered pairs of positive integers with and , satisfy ?

### Key Concepts

Number theory

Orderd Pair

LCM

PRMO-2019, Problem 18

Pre College Mathematics

## Try with Hints

At first we assume that

where & are co-prime

Therefore ,

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

Therefore we can say that

when (for ),No solution
when to ,7 solution
when, to ,13 solution
Can you finish the problem........

Therefore Total solutions =

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Try this beautiful problem from PRMO, 2019, Problem 18 based on Ordered Pairs.

## Orderd Pairs | PRMO | Problem-18

How many ordered pairs of positive integers with and , satisfy ?

### Key Concepts

Number theory

Orderd Pair

LCM

PRMO-2019, Problem 18

Pre College Mathematics

## Try with Hints

At first we assume that

where & are co-prime

Therefore ,

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

Therefore we can say that

when (for ),No solution
when to ,7 solution
when, to ,13 solution
Can you finish the problem........

Therefore Total solutions =

## Subscribe to Cheenta at Youtube

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### 2 comments on “Ordered Pairs | PRMO-2019 | Problem 18”

1. Mukunda says:

Why can't you consider p as 15 and q as 33

1. Mukunda says:

Sorry I got it.. Never mind