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MathNet 2020 — Math Olympiad Vault — Part 05 Question 62

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 05

Question 62

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be an odd function, that is, a function satisfying $-f(x)=f(-x)$ for every $x \in \mathbb{R}$. Suppose that $f(x+5)=f(x)$ for every $x \in \mathbb{R}$ and that $f(1 / 3)=1$. Find the value of the sum:
$$
f(16 / 3)+f(29 / 3)+f(12)+f(-7)
$$