Page 228 of Claim Me
"For someone who talks about systems, that’s a weak piece! All that supposed brilliance, and you end up relying on silly little Gabs?"
Damn, his words drip with such contempt for me. I had no idea it went that deep… Well, it’s obvious, those one and a half years I spent being in love with Marcel were simply wasted. The problem is I only have myself to blame.
I shift my gaze to Blue. Fate chose him for me, and I won’t fail him today.
Our eyes meet.
He sends me a small, encouraging smile, almost warm. And I respond with a matching smile.
Then he says,
"You removed Gabriel from your model because you couldn’t quantify him," he says. "Incompetence on your side."
Marcel’s eyes flash.
"You’re crazy."
Blue speaks slowly, almost carefully, "The heart aspect. You were unable to harvest what love could give you because you failed to see its power. And it can give… a lot."
Strange, it almost doesn’t seem to be entirely directed at Marcel…
Marcel snorts, then straightens up, and a deep frown forms on his forehead.
He starts to pace in front of us like he needs the movement to hold himself together, and I keep my eyes on Blue because he doesn’t move at all, like the ropes, the chair, and our entire situation are some kind of chessboard.
Marcel abruptly stops and looks straight at him.
"The puzzle you mentioned. I doubt that silly alpha can solve anything, but you… you’re something else. I have faith in you," he says sarcastically. "Let’s see if your reputation is actually earned."
Blue doesn’t answer, he just looks back at him as if he already knows how this ends.
Marcel pulls out his phone, checks something, then puts it away. Only after that does he start speaking, slower now, like he wants every word to land.
"Let’s start simple," Marcel says, and there’s confidence in it, the kind that sounds like he’s sure he will win. "Something mathematical."
Blue still doesn’t react. Marcel takes a slow step, eyes fixed on him.
"You’re given a function on the positive integers," he says. "Defined recursively. f of one equals one."
I raise a brow when I hear the challenge forming, because it sounds like it goes beyond what Marcel actually studies, but… who knows. His major is philosophy, sure, but his minor is formal logic. Marcel has always gravitated toward things that resemble proofs, clean, structured arguments rather than tedious, step-by-step calculations. He likes problems that reward strategy and pattern recognition without requiring constant practice with numbers. To his credit, Marcel never needed help with math, not like Edgar did. He understood it well enough to apply it to more abstract assignments, which makes me curious about what I’m about to see.
Marcel’s brows furrow, and his lips purse slightly as he continues,
"For every n, f of n plus one equals f of n plus the number of divisors of n."
I follow it without losing the thread. I see the structure, the dependency, the way each step builds on the last, but it’s dense in a way that would take some time to unpack, the kind of thing you don’t solve on instinct, especially while being kidnapped and threatened with death by a metal cord…
Marcel keeps going, his tone slightly haughty. "So at each step you add the divisor count. Nothing hidden, no tricks, just accumulation."
He looks at Blue smugly. "My question is simple. Describe the growth. Not numerically, but structurally. What does this converge to, in behavior if not in form?"
There’s something in the way he frames it, like he’s less interested in the answer itself and more in whether Blue can justify one, whether he can produce something that holds up. He squares his shoulders combatively, but Blue just exhales, almost bored.
"It grows on the order of n log n," he says. "More precisely, it behaves like n log n plus a linear correction term, coming from the average order of the divisor function."
Marcel’s jaw sets. "That’s not a description. That’s a claim."
Blue’s gaze doesn’t falter. "It’s the average order of the divisor function," he replies. "You’re summing it."
