In practice, many options can be given:
Consider X + Y, then compute X - Y.
Given X + Y, find X - Y
Compute the following: X + Y, given X - Y.
However, you'll often see alone expressions like find, compute, determine because it's probably stated in a direct form what's about to be solved/calculated.
In maths, there's no rule for people to choose just one way to state what they want to write. As long as the sense and goal are clear, you can put whatever you want.
As for OP's example, we can state
Given: two integers a and b
Find, if possible: integers x and y such that ax + by = gcd(a, b); or
Find, if they exist: integers x and y such that ax + by = gcd(a, b); or
Assuming that x and y are integers, determine if ax + by = gcd(a, b).
I think love interests or romantic interests could work, given OP's latest context.
From tvtropes.org,
Love Interest
The princess to be rescued, or the Prince Charming to sweep the heroine off her feet. Or just someone that happens to become romantically involved.
It's a Super Trope so universal, that there are too many specific examples to list. There are a few in the list below.
The list includes Girl Next Door, Girl of My Dreams, and Hello, Nurse!.
When applied to real life, I think love interest is just as flexible. A love interest is basically a person that you are romantically interested in. This could range from something small, like going on a few dates, to something big, like love and marriage.
A romantic interest is similar to a love interest, with the possible nuance that a romantic interest concerns more casual relationships.
I wasn't able to find any reputable dictionary sources, so I imagine that the definitions vary from one person's opinion to another. However, if you call these girls your love interests, I think people will get the point that you are interested in them romantically or that you pursuing them romantically to some degree as described above.
By the way, you could also say that you are interested in these girls, or into them. They mean that you have a some kind of romantic interest in them, though it suggests a casual one. I don't think it would include "loving" someone, unless it's unrequited love.
Best Answer
You could call it requester, a noun derived from request meaning "the entity that did the requesting". (requestor is an alternative, less-common variant).
Or, since it's in a programming context, you could use caller since presumably the "requested by" object called a constructor to create the requested object.
Finally, you could go simple with creator.