perplexus.info :: Calculus : An increasing function equation

An increasing function equation (Posted on 2021-01-24)

Find all strictly increasing functions f:N->N such that (f(x) + f(y))/(1 + f(x + y)) is a non-zero natural number, for all x, y∈N.

No Solution Yet Submitted by Danish Ahmed Khan

Rating: 3.0000 (1 votes)

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A family of functions

| Comment 1 of 2

f(x) = kx + 1 works, where k is an integer > 0

Then (f(x) + f(y))/(1 + f(x + y)) = 1

I don't offhand see anything else that works.

Posted by Steve Herman on 2021-01-24 20:22:37

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