User:Vincent Lextrait

I am contributor to the French pages of Wikipedia.

Dashes
A frequent mistake is to add spaces around em dashes. In case of doubt: Manual for dashes.

MAD
I have been, in 1984, the co-author with Bruno Chabrier of MAD.

Question 6 generalized
$$\frac{a^n+b^n}{\displaystyle\sum_{i=2}^n\sum_{j=1}^{i-1}a^{i-j}b^j+1}$$ with $$(a ; b) \in {\N^+}^2, n \in \N, n\geq 2$$, when it yields a result in $$\N$$, is always a power of $$n$$.

Question 6 is the case where $$n$$ is 2.

When $$n$$ is 3, there are only two solutions (symmetry put aside): $$(1 ; 2)$$ and $$(7 ; 9)$$, both yielding $$1=1^3$$.

When $$n>3$$, there are no solutions.

Incompressible real numbers
Let I be the set of real numbers with an infinite Kolmogorov complexity. I is the set of incompressible numbers. Show that I is dense in $\R$.

Software development index
The software development index of a developer for a given programming language is the average number of lines of code written in that language that turn out to be bug free. The whole mankind is between 3 and 20.