Try this beautiful problem from Algebra based on Largest Common Divisor .

## Largest Common Divisor | PRMO | Problem 11

For natural numbers x and y,let (x,y) denote the largest common divisor of x and y. How many pairs of natural numbers x and y with x≤y satisfy the equation xy=x+y+(x,y)?

Answer:

PRMO-2018, Problem 21

Pre College Mathematics

## Try with Hints

At first we have to find out the divisors that satisfy the equation .so we assume that =ak and =bk and try to find out the divisors

Can you now finish the problem ....

Let =ak and =bk, then (x,y)=k and (a,b)=1

Therefore

Can you finish the problem...

For , then (b-1) divides 2

Therefore a=1+2=3 and a=1+1=2

Now for

so

Therefore

Therefore

Hence total number of pairs =3

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Try this beautiful problem from Algebra based on Largest Common Divisor .

## Largest Common Divisor | PRMO | Problem 11

For natural numbers x and y,let (x,y) denote the largest common divisor of x and y. How many pairs of natural numbers x and y with x≤y satisfy the equation xy=x+y+(x,y)?

Answer:

PRMO-2018, Problem 21

Pre College Mathematics

## Try with Hints

At first we have to find out the divisors that satisfy the equation .so we assume that =ak and =bk and try to find out the divisors

Can you now finish the problem ....

Let =ak and =bk, then (x,y)=k and (a,b)=1

Therefore

Can you finish the problem...

For , then (b-1) divides 2

Therefore a=1+2=3 and a=1+1=2

Now for

so

Therefore

Therefore

Hence total number of pairs =3

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