Let $f$ be a periodic continuous function on $\mathbb R$ with period $1$. Let $a$ be any real number. Prove that there exists a real number $x$ with $f(x+a)=f(x)$.
Let $f$ be a periodic continuous function on $\mathbb R$ with period $1$. Let $a$ be any real number. Prove that there exists a real number $x$ with $f(x+a)=f(x)$.
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