MathDB

Problem 4

Part of 2004 VJIMC

Problems(2)

m+n and mn+1 powers of 2

Source: VJIMC 2004 1.4

7/8/2021
Find all pairs (m,n)(m,n) of positive integers such that m+nm+n and mn+1mn+1 are both powers of 22.
Diophantine equationnumber theory
exists n f^(n)(x)=0 implies f is a polynomial if f is analytic

Source: VJIMC 2004 2.4

7/12/2021
Let f:R→Rf:\mathbb R\to\mathbb R be an infinitely differentiable function. Assume that for every x∈Rx\in\mathbb R there is an n∈Nn\in\mathbb N (depending on xx) such that f(n)(x)=0.f^{(n)}(x)=0.Prove that ff is a polynomial.
algebrapolynomialreal analysis