Try this beautiful problem from Algebra based on Largest Common Divisor .
For natural numbers
Answer:
PRMO-2018, Problem 21
Pre College Mathematics
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
Try this beautiful problem from Algebra based on Largest Common Divisor .
For natural numbers
Answer:
PRMO-2018, Problem 21
Pre College Mathematics
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