grandes-ecoles 2016 QIV.B.1

grandes-ecoles · France · centrale-maths2__pc Proof Deduction or Consequence from Prior Results

We consider throughout the rest of this part a real $\alpha$. We assume that for every prime number $p$, $p^\alpha$ is a natural number. We propose to show that $\alpha$ is then a natural number.
Show that for every integer $k$ strictly positive, $k^\alpha$ belongs to $\mathbb{N}^*$.

We consider throughout the rest of this part a real $\alpha$. We assume that for every prime number $p$, $p^\alpha$ is a natural number. We propose to show that $\alpha$ is then a natural number.

Show that for every integer $k$ strictly positive, $k^\alpha$ belongs to $\mathbb{N}^*$.

Paper Questions

QI.A.1 QI.A.2 QI.A.3 QI.A.4 QI.A.5 QI.A.6 QI.A.7 QI.A.8 QI.A.9 QI.B.1 QI.B.2 QI.B.3 QI.B.4 QI.B.5 QI.B.6 QI.B.7 QII.A.1 QII.A.2 QII.A.3 QII.B.1 QII.B.2 QII.B.3 QII.B.4 QII.C QIII.A.1 QIII.A.2 QIII.A.3 QIII.A.4 QIII.A.5 QIII.B.1 QIII.B.2 QIII.B.3 QIII.C.1 QIII.C.2 QIII.C.3 QIII.C.4 QIII.C.5 QIV.A.1 QIV.A.2 QIV.A.3 QIV.A.4 QIV.B.1 QIV.B.2 QIV.B.3 QIV.C.1 QIV.C.2 QIV.C.3