MathDB

1

Part of 2022 Francophone Mathematical Olympiad

Problems(2)

number theory involing floor of sqrt(n)

Source: P1 : franchophone math olymp junior 2022

5/23/2022
find all the integer n≥1n\geq1 such that ⌊n⌋∣n\lfloor\sqrt{n}\rfloor \mid n
number theory
functional equation from Z to Z

Source: P1 francophone math olympiad senior 2022

5/23/2022
find all functions f:Z→Zf:\mathbb{Z} \to \mathbb{Z} such that f(m+n)+f(m)f(n)=n2(f(m)+1)+m2(f(n)+1)+mn(2−mn)f(m+n)+f(m)f(n)=n^2(f(m)+1)+m^2(f(n)+1)+mn(2-mn) holds for all m,n∈Zm,n \in \mathbb{Z}
algebrafunctional equationfunction