UPSC CDS Math HCF and LCM of Numbers and Polynomials Questions

Set of integral numbers is the union of Set of whole numbers and Set of negative natural numbers. There can be infinitely many pairs of number (a, b) such that HCF (a,b)=5 and a+b=65.
For Example
HCF (5,60)=5 and 5+60=65
HCF (105,–40)=5
and 105–40=65
HCF (60,5)=5 and 60+5=65
∴ We can find infinite numbers ofsolutions.