Question

if p and q are relatively prime numbers such that p+q=10 and p<q.how many such pairs are possible​

Answer 1

Answer:

2 pairs possible,i.e;(1,9),(3,7)

Answer 2

Answer:

as p and q relative prime numbers.

if we consider positive prime numbers, then 2 cases possible

1 and 9

3 and 7

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Special case

If p is a prime number, -p is prime too.

So, In this case, there are infinite pairs of p and q that satisfy the conditions.

There are only solutions where both p and q are primes so, provided they are not equal, they are also relatively prime. The simplest ones are detailed below:

3, 7

-3, 13

-7, 17

-13, 23

-19, 29

-31, 41

and many more...