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MATH / The function f satisfies the functional equation

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

The function ff satisfies the functional equation f(x)+f(y)=f(x+y)−xy−1f(x) + f(y) = f(x + y) - xy - 1for all real numbers xx and y.y. If f(1)=1,f(1) = 1, then find all integers nn such that f(n)=n.f(n) = n. Enter all such integers, separated by commas.
Plain-text mathematical notation (without MathML)
The function f satisfies the functional equation
f(x)+f(y)=f(x+y)−xy−1for all real numbers x and y.  If f(1)=1, then find all integers n such that f(n)=n.  Enter all such integers, separated by commas.
Original LaTeX notation
The function $f$ satisfies the functional equation
\[f(x) + f(y) = f(x + y) - xy - 1\]for all real numbers $x$ and $y.$  If $f(1) = 1,$ then find all integers $n$ such that $f(n) = n.$  Enter all such integers, separated by commas.

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
2922569f-5b78-5692-860d-6e6693319006
task_key
intermediate~5falgebra--test--2922569f-5b78-5692-860d-6e6693319006
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import