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- Sun Mar 28, 2021 12:40 pm
- Forum: Divisional Math Olympiad
- Topic: BdMO Regional 2021 Higher Secondary P8
- Replies: 16
- Views: 12265
Re: Solution to BdMO Regional 2021 Higher Secondary P8
Observe that, $f(x)-x\not\equiv0\pmod{3}$ $\Longleftrightarrow f(x)\not\equiv x\pmod{3}$ Claim : $f$ is bijective. $f$ is injective (one-one) : $f(a)=f(b)$ $\Longrightarrow f(f(a))=f(f(b))$ $\Longrightarrow a=b$ $f$ is surjective (onto) : Let $y\in S$. Let $x=f(y)$. Then $f(x)=y$. Since $f$ is bije...