（難問）eが二次方程式の解ではない事を証明せよ

訂正

So we know that e^4 is irrational; to show that e^3 , e^5 etc. are irrational as well,
we need heavier machinery (that is, a bit of calculus), and a new idea - which essentially
goes back to Charles Hermite, and for which the key is hidden in the following simple lemma.