diff --git a/6_number.jl b/6_number.jl
new file mode 100644
index 0000000000000000000000000000000000000000..194e33f70a1941f7f81cf408993685cbe296ecd9
--- /dev/null
+++ b/6_number.jl
@@ -0,0 +1,471 @@
+### A Pluto.jl notebook ###
+# v0.19.46
+
+using Markdown
+using InteractiveUtils
+
+# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
+macro bind(def, element)
+    quote
+        local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
+        local el = $(esc(element))
+        global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
+        el
+    end
+end
+
+# ╔═╡ 06679a09-47d7-4024-8232-4954c08747a0
+using PlutoUI, Primes
+
+# ╔═╡ 1b1d5c9b-5fc7-480e-9649-e9c44a49c38d
+include("utils.jl")
+
+# ╔═╡ 736307ec-a2a4-11ef-0f85-ad1a0093e06a
+md"# La théorie des nombres"
+
+# ╔═╡ cbabee34-2ca2-4ad4-93ba-2ec3c941da5e
+md"""
+Si tous les mois avaient 30 jours, est-ce qu'il y a des jours de la semaine qui ne seront jamais le premier du mois ?
+
+Reformulation: pour tout nombre ``0 \le j < 7``, existe-t-il ``x`` et ``y`` tels que ``30x = j + 7y``. Notation modulo : ``30x \equiv j \pmod{7}``.
+
+Si tous les ans avaient 365 jours, est-ce qu'il y a des jours de la semaine qui ne seront jamais le jours de Noël ? Est si tous les ans avaient 366 jours ? Et s'ils avaient 364 jours ?
+
+Reformulation: pour tout nombre ``0 \le j < 7``, existe-t-il ``x`` et ``y`` tels que ``365x = j + 7y``. Notation modulo : ``365x \equiv j \pmod{7}``.
+"""
+
+# ╔═╡ 909b8a36-79bb-4c1a-9dd7-4acaffc0434e
+frametitle("Théorème de Bézout")
+
+# ╔═╡ 08b18315-c28e-44ed-beb2-5b17421b0224
+md"""
+> **Définition** Le *Greatest Common Divisor (GCD)* de deux nombres ``a \in \mathbb{Z}`` et ``b \in \mathbb{Z}``, noté ``\text{gcd}(a, b)`` est le plus grand nombre ``g \in \mathbb{Z}`` qui divise ``a`` et ``b``. C'est à dire qu'il existe ``x \in \mathbb{Z}`` tel que ``a = gx`` et ``y \in \mathbb{Z}`` tel que ``b = gy``. En notation modulaire, ``a \equiv 0 \pmod{g}`` et ``b \equiv 0 \pmod{g}``.
+
+> **Théorème de Bézout** Il existe ``x, y \in \mathbb{Z}`` tels que ``ax + by = c`` si et seulement si ``\text{gcd}(x, y)`` divise ``c``. En notation modulaire ``ax \equiv c \pmod{b}`` et ``by \equiv c \pmod{a}``.
+"""
+
+# ╔═╡ 7bad8c6c-45c7-402f-ad59-6857e9268901
+qa(md"Comment prouver que l'égalité ``ax + by = c`` implique que ``\text{gcd}(x, y)`` divise ``c`` ?",
+md"""
+""",)
+
+# ╔═╡ cd481f6c-66f4-4ebf-9769-c3edc24f403b
+frametitle("Algorithme d'Euclide : élaboration")
+
+# ╔═╡ 37585789-bd43-4ce5-b550-ad712b70d226
+md"""
+> **Définition** Le résultat de la *division Euclidienne* de ``a`` par un diviseur ``d`` est un quotient ``q`` et un reste ``0 \le r < d`` tels que ``a = qd + r``. En notation modulaire ``a \equiv r \pmod{d}``.
+"""
+
+# ╔═╡ 6e59ee60-ef73-45ca-86eb-4d8a44c73771
+qa(md"**Observation clé** Que dit le théorème de Bézout par rapport à ``\text{gcd}(a, d)`` et ``r``.",
+md"""
+Le reste ``r`` est **divisible** par ``\text{gcd}(a, d)``.
+Le nombre ``\text{gcd}(a, d)`` divise donc les 3 nombres, ``a``, ``d`` et ``r`` et donc ``\text{gcd}(a, d) = \text{gcd}(a, d, r)``.
+""")
+
+# ╔═╡ d6b89fda-308f-43da-8028-1a812b4516cf
+qa(md"**Observation clé** Que dit le théorème de Bézout par rapport à ``\text{gcd}(d, r)`` et ``a``.",
+md"""
+Le nombre ``a`` est **divisible** par ``\text{gcd}(d, r)``.
+Le nombre ``\text{gcd}(d, r)`` divise donc les 3 nombres, ``a``, ``d`` et ``r`` et donc ``\text{gcd}(d, r) = \text{gcd}(a, d, r)``.
+En combinant ça avec l'observation précédente, on a le résultat suivant.``\text{gcd}(a, d) = \text{gcd}(d, r)``.
+""")
+
+# ╔═╡ d1b260fb-7500-47fb-bb48-21b5857ab55a
+md"""
+**Lemme**: Si ``a \equiv r \pmod{b}`` alors ``\text{gcd}(a, b) = \text{gcd}(b, r)``.
+"""
+
+# ╔═╡ 9207b107-e1b0-4328-a004-f4b8152b423f
+qa(md"**Observation clé** Si ``a > b``, trouver un mono-variant.",
+md"""
+On a ``(a, b) > (b, r)``. En effet, ``a > b`` par supposition et ``b > r`` par définition de l'algorithme d'Euclide.
+Notons que même si la supposition ``a > b`` n'est pas vraie, elle le devient pour ``\text{gcd}(b, r)``.
+""")
+
+# ╔═╡ 48eba223-6cce-4aa2-9977-4883ba7903fc
+qa(md"**Observation finale** Si ``a`` et ``b`` sont positifs et qu'on effectue la substitution ``(a, b) \to (b, r)`` récursivement, le mono-variant impose qu'on ne puisse itérer qu'un nombre fini de fois, que va-t-il se passer ?",
+md"""
+La paire ``(a, b)`` va diminuer strictement (c'est à dire d'au moins 1) à chaque itération. Pourtant, ce sont des nombres entier positifs donc ils ne peuvent diminuer strictement qu'un nombre fini de fois. C'est une contradiction, comme cela se fait-il ?
+À un moment ``b`` vaudra 0, on ne pourra alors plus faire de division Euclidienne. On utilisera alors le fait que ``\text{gcd}(a, 0) = a``.
+""")
+
+# ╔═╡ bd0c0258-7040-42e7-a20e-532b55af3a62
+frametitle("Algorithme d'Euclide : implémentation")
+
+# ╔═╡ 97736c6a-3f5d-4978-8dd2-0a11c09ba9f0
+function pgcd(a, b)
+	print("gcd($a, $b) = ")
+    if a < b
+		return pgcd(b, a)
+	elseif b == 0
+		println(a)
+		return a
+	else
+		return pgcd(b, mod(a, b))
+	end
+end
+
+# ╔═╡ 1a4da418-147f-46f4-9b95-7955183aa5cf
+md"a = $(@bind a Slider(1:typemax(Int32), default=90284599, show_value = true))"
+
+# ╔═╡ f39cccac-5b24-46e4-8749-1b0a944542ef
+md"b = $(@bind b Slider(1:typemax(Int32), default=249357461, show_value = true))"
+
+# ╔═╡ fe2af566-4a8b-4052-9915-85266ee5ce98
+pgcd(a, b)
+
+# ╔═╡ 03e49669-cdee-4241-862d-33ee91214455
+md"The complexity is difficult to evaluate but can be shown to be ``O(\log(\min(a, b)))``."
+
+# ╔═╡ 83852dd5-3546-45af-a845-b01dab0aa2a6
+frametitle("Division modulaire")
+
+# ╔═╡ 352b26e4-1cc3-47d5-a772-b460f718ebf8
+frametitle("Inverse modulaire")
+
+# ╔═╡ 2cb5c6e0-b431-4d2e-b023-cd2131112eca
+frametitle("Algorithme d'Euclide étendu")
+
+# ╔═╡ f4895654-d684-42d2-ae4c-de72e6824484
+frametitle("Euler totient function")
+
+# ╔═╡ f855a589-36c2-4b77-9f01-17da963658f4
+mod(2^Primes.totient(11), 11)
+
+# ╔═╡ 457a1da2-3f87-43e6-a9cf-8dbfb225c4dc
+frametitle("Fast exponentiation")
+
+# ╔═╡ 00000000-0000-0000-0000-000000000001
+PLUTO_PROJECT_TOML_CONTENTS = """
+[deps]
+PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
+Primes = "27ebfcd6-29c5-5fa9-bf4b-fb8fc14df3ae"
+
+[compat]
+PlutoUI = "~0.7.60"
+Primes = "~0.5.6"
+"""
+
+# ╔═╡ 00000000-0000-0000-0000-000000000002
+PLUTO_MANIFEST_TOML_CONTENTS = """
+# This file is machine-generated - editing it directly is not advised
+
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+# ╟─cbabee34-2ca2-4ad4-93ba-2ec3c941da5e
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diff --git a/utils.jl b/utils.jl
new file mode 100644
index 0000000000000000000000000000000000000000..9b289cb36453573b68d4512e6608199599fd1b39
--- /dev/null
+++ b/utils.jl
@@ -0,0 +1,83 @@
+begin
+    function CenteredBoundedBox(str)
+        xbearing, ybearing, width, height, xadvance, yadvance =
+            Luxor.textextents(str)
+        lcorner = Point(xbearing - width/2, ybearing)
+        ocorner = Point(lcorner.x + width, lcorner.y + height)
+        return BoundingBox(lcorner, ocorner)
+    end
+    function boxed(str::AbstractString, p)
+        translate(p)
+        sethue("lightgrey")
+        poly(CenteredBoundedBox(str) + 5, action = :stroke, close=true)
+        sethue("black")
+        text(str, Point(0, 0), halign=:center)
+        #settext("<span font='26'>$str</span>", halign="center", markup=true)
+        origin()
+    end
+
+    # `Cols` conflict with `DataFrames`
+    struct HAlign{T<:Tuple}
+        cols::T
+        dims::Vector{Int}
+    end
+    function HAlign(a::Tuple)
+        n = length(a)
+        return HAlign(a, div(100, n) * ones(Int, n))
+    end
+    HAlign(a, b, args...) = HAlign(tuple(a, b, args...))
+
+    function Base.show(io, mime::MIME"text/html", c::HAlign)
+        x = div(100, length(c.cols))
+    	write(io, """<div style="display: flex; justify-content: center; align-items: center;">""")
+        for (col, p) in zip(c.cols, c.dims)
+            write(io, """<div style="flex: $p%;">""")
+            show(io, mime, col)
+            write(io, """</div>""")
+        end
+    	write(io, """</div>""")
+    end
+    function imgpath(file)
+        if !('.' in file)
+            file = file * ".png"
+        end
+        return joinpath(joinpath(@__DIR__, "images", file))
+    end
+    function img(file, args...)
+        LocalResource(imgpath(file), args...)
+    end
+    section(t) = md"# $t"
+    frametitle(t) = md"# $t" # with `##`, it's not centered
+
+    struct Join
+		list
+	    Join(a) = new(a)
+	    Join(a, b, args...) = Join(tuple(a, b, args...))
+    end
+	function Base.show(io::IO, mime::MIME"text/html", d::Join)
+		for el in d.list
+			show(io, mime, el)
+		end
+	end
+
+	struct HTMLTag
+		tag::String
+		parent
+	end
+	function Base.show(io::IO, mime::MIME"text/html", d::HTMLTag)
+		write(io, "<", d.tag, ">")
+		show(io, mime, d.parent)
+		write(io, "</", d.tag, ">")
+	end
+
+    function qa(question, answer)
+        return HTMLTag("details", Join(HTMLTag("summary", question), answer))
+    end
+
+    function qa(question::Markdown.MD, answer)
+        # `html(question)` will create `<p>` because `question.content[]` is `Markdown.Paragraph`
+        # This will print the question on a new line and we don't want that:
+        h = HTML(sprint(Markdown.htmlinline, question.content[].content))
+        return qa(h, answer)
+    end
+end