a computational problem is understood to be a task that is in principle amenable to being solved by a computer (i.e. the problem can be stated by a set of mathematical instructions). Informally, a computational problem consists of problem instances and solutions to these problem instances. For example, primality testing is the problem of determining whether a given number is prime or not. The instances of this problem are natural numbers, and the solution to an instance is yes or no based on whether the number is prime or not.
... A key distinction between analysis of algorithms and computational complexity theory is that the former is devoted to analyzing the amount of resources needed by a particular algorithm to solve a problem, whereas the latter asks a more general question about all possible algorithms that could be used to solve the same problem.
So a problem can be solved by multiple algorithms.
I was wondering if an algorithm can solve different problems, or can only solve one problem? Note that I distinguish a problem and its instances as in the quote.