MathDB

P5

Part of 2023 Bangladesh Mathematical Olympiad

Problems(2)

Find the minimum

Source: BdMO 2023 Secondary National P5

2/12/2023
Let mm, nn and pp are real numbers such that (m+n+p)(1m+1n+1p)=1\left(m+n+p\right)\left(\frac 1m + \frac 1n + \frac1p\right) =1. Find all possible values of 1(m+n+p)2023−1m2023−1n2023−1p2023.\frac 1{(m+n+p)^{2023}} -\frac 1{m^{2023}} -\frac 1{n^{2023}} -\frac 1{p^{2023}}.
algebraManipulationidentity
Integrable Function

Source: BdMO 2023 Higher Secondary National P5

2/12/2023
Consider an integrable function f:R→Rf:\mathbb{R} \rightarrow \mathbb{R} such that af(a)+bf(b)=0af(a)+bf(b)=0 when ab=1ab=1. Find the value of the following integration: ∫0∞f(x) dx \int_{0}^{\infty} f(x) \,dx
algebraintegrationfunctional equationfunction