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f'(a) > 0
f(a)f(b) = f(ab)
f(2) = 2

\[f(2) = f(1 \times 2) = f(1)f(2)\]
hence f(1) = 1

Be careful with your derivatives. This is not a continuous function.

ah no it isnt

i should have said
x ≥ y, then f(x) ≥ f(y)

i was thinking induction?

That's what I first thought as well, but for induction to work, you need to show that \(f(3)=3\).

f(2^n) = 2^n
doesn't particularly help

thats it i think

ah

i did not know that

not having any luck. i tried using the fact that consecutive integers are coprime

let me know if you want a hint.

i think i'll sleep on it, im too tired to do maths now lol

f(3)f(5)=f(15)

That's clever. Significantly more simple than the solution I had.