Moved links to margin. Added more links

collects/math/scribblings/math-number-theory.scrbl

@@ -31,6 +31,7 @@
 @; ----------------------------------------
 @section[#:tag "congruences"]{Congruences and Modular Arithmetic}
 
+@margin-note{Wikipedia: @hyperlink["http://en.wikipedia.org/wiki/Divisor"]{Divisor}}
 @defproc[(divides? [m Integer] [n Integer]) boolean?]{
    Returns @racket[#t] if @racket[m] divides @racket[n],
    @racket[#f] otherwise.
@@ -42,10 +43,9 @@
    @interaction[#:eval untyped-eval
                        (require math)
                        (divides? 2 9)]   
-   
-   @; http://en.wikipedia.org/wiki/Divisor
 }   
 
+@margin-note{Wikipedia: @hyperlink["http://en.wikipedia.org/wiki/B%C3%A9zout's_identity"]{Bezout's Identity}}
 @defproc[(bezout [a Integer] [b Integer] [c Integer] ...) (Listof Integer)]{
   Given integers @racket[a], @racket[b], @racket[c] ... 
   returns a list of integers @racket[u], @racket[v], @racket[q] ... 
@@ -56,9 +56,9 @@
   @interaction[#:eval untyped-eval
                       (bezout 6 15)
                       (+ (* -2 6) (* 1 15))]
-  @; http://en.wikipedia.org/wiki/B%C3%A9zout's_identity
 }
   
+@margin-note{Wikipedia: @hyperlink["http://en.wikipedia.org/wiki/Coprime"]{Coprime}}
 @defproc[(coprime? [a Integer] [b Integer] ...) boolean?]{
   Returns @racket[#t] if the integers @racket[a],@racket[b],... are coprime.
 
@@ -68,19 +68,19 @@
   The numbers 2, 6, and, 15 are coprime.
   @interaction[#:eval untyped-eval
                       (coprime? 2 6 15)]
-  @; http://en.wikipedia.org/wiki/Coprime
 }  
 
  
+@margin-note{Wikipedia: @hyperlink["http://en.wikipedia.org/wiki/Pairwise_coprime"]{Pairwise Coprime}}
 @defproc[(pairwise-coprime? [a Integer] [b Integer] ...) boolean?]{
   Returns @racket[#t] if the integers @racket[a],@racket[b],... are pairwise coprime.
 
   The numbers 2, 6, and, 15 are not pairwise coprime, since 2 and 6 share the factor 3.
   @interaction[#:eval untyped-eval
                       (pairwise-coprime? 2 6 15)]
-  @; http://en.wikipedia.org/wiki/Pairwise_coprime
 }  
 
+@margin-note{Wikipedia: @hyperlink["http://en.wikipedia.org/wiki/Modular_multiplicative_inverse"]{Multiplicative Inverse}}
 @defproc[(modular-inverse [a Integer] [n Integer]) natural?]{
   Returns the inverse of @racket[a] module @racket[n],
   if @racket[a] and @racket[n] are coprime,
@@ -97,12 +97,12 @@
   The number 0 has no inverse modulo 5.
   @interaction[(require math)
                (modular-inverse 0 5)]
-  @; http://en.wikipedia.org/wiki/Modular_multiplicative_inverse
 }  
 
 
 
 @defproc[(solve-chinese [as (Listof Integer)] [bs (Listof Integer)]) natural?]{
+  @margin-note{Wikipedia: @hyperlink["http://en.wikipedia.org/wiki/Chinese_remainder_theorem"]{Chinese Remainder Theorem}}
   Given a list of integers @racket[as] and a list of coprime moduli @racket[ns]
   the function @racket[solve-chinese] will return
   the single natural solution @racket[x] in @racket[{0,...,n-1}]
@@ -120,8 +120,6 @@
   when divided by 7 leaves a remainder of 2? 
   @interaction[#:eval untyped-eval
                       (solve-chinese '(2 3 2) '(3 5 7))]  
-  
-  @; http://en.wikipedia.org/wiki/Chinese_remainder_theorem
 }
 
 @defproc[(quadratic-residue? [a natural?] [n natural?]) boolean?]{
@@ -400,6 +398,7 @@ for all coprime natural numbers @racket[a] and @racket[b].
 The functions @racket[totient], @racket[moebius-mu], and, 
 @racket[divisor-sum] are multiplicative.
 
+@margin-note{Wikipedia: @hyperlink["http://en.wikipedia.org/wiki/Euler%27s_totient_function"]{Euler's Totient}}
 @defproc[(totient [n Natural]) natural?]{
 Returns the number of integers from 1 to @racket[n]
 that are coprime with @racket[n].
@@ -412,12 +411,13 @@ Note: The function @racket[totient] is multiplicative.
                     (require racket/function) ; for curry
                     (totient 9)
                     (length (filter (curry coprime? 9) (range 10)))]
-
-@; http://en.wikipedia.org/wiki/Euler%27s_totient_function
 }
 
 
+
+
 @defproc[(moebius-mu [n Natural]) (Union -1 0 1)]{
+@margin-note{Wikipedia: @hyperlink["http://en.wikipedia.org/wiki/M%C3%B6bius_function"]{Moebius Function}}
 Returns:
 
 @racket[1]  if @racket[n] is a product of an even number of primes
@@ -432,11 +432,10 @@ Note: The function @racket[moebius-mu] is multiplicative.
                     (moebius-mu (* 2 3 5))
                     (moebius-mu (* 2 3 5 7))
                     (moebius-mu (* 2 2 3 5 7))]
-
-@; http://en.wikipedia.org/wiki/M%C3%B6bius_function
 }
 
 
+@margin-note{Wikipedia: @hyperlink["http://en.wikipedia.org/wiki/Divisor_function"]{Divisor Function}}
 @defproc[(divisor-sum [n Natural] [k Natural]) natural?]{
 Returns sum of the @racket[k]th powers of 
 all divisors of @racket[n].
@@ -446,37 +445,32 @@ Note: The function @racket[divisor-sum] is multiplicative.
 @interaction[#:eval untyped-eval         
                     (divisor-sum 12 2)
                     (apply + (map sqr (divisors 12)))]
-
-@; http://en.wikipedia.org/wiki/Divisor_function
 }
 
 
 @; ----------------------------------------
 @section[#:tag "number-sequences"]{Number Sequences}
 
+@margin-note{Wikipedia: @hyperlink["http://en.wikipedia.org/wiki/Bernoulli_number"]{Bernoulli Number}}
 @defproc[(bernoulli [n Natural]) exact-rational?]{
   Returns the @racket[n]th Bernoulli number.
-  Definition:
+
-  @url{http://en.wikipedia.org/wiki/Bernoulli_number}.
 
   @interaction[#:eval untyped-eval
                       (map bernoulli (range 9))]
 }
 
+@margin-note{MathWorld: @hyperlink["http://mathworld.wolfram.com/EulerianNumber.html"]{Eulerian Number}}
 @defproc[(eulerian-number [n Natural] [k Natural]) natural?]{
   Returns the Eulerian number @math-style{<n,k>}.
-  Definition:
-  @url{http://mathworld.wolfram.com/EulerianNumber.html}.
 
   @interaction[(require math racket)
                (eulerian-number 5 2)]
 }
 
+@margin-note{Wikipedia: @hyperlink["http://en.wikipedia.org/wiki/Fibonacci_number"]{Fibonacci Number}}
 @defproc[(fibonacci [n Natural]) natural?]{
   Returns the @racket[n]th Fibonacci number.
-  See 
-  @url{http://en.wikipedia.org/wiki/Fibonacci_number}
-  for a definition.
 
   The ten first Fibonacci numbers.
   @interaction[(require math racket)
@@ -502,9 +496,10 @@ are less than or equal to @racket[n].
                (farey 3)]
 }
 
+@margin-note{MathWorld: @hyperlink["http://mathworld.wolfram.com/TangentNumber.html"]{Tangent Number}}
 @defproc[(tangent-number [n integer?]) integer?]{
 Returns the @racket[n]th tangent number.
-See @url{http://mathworld.wolfram.com/TangentNumber.html} for a definition.
+            
   @interaction[(require math)
                (tangent-number 1)
                (tangent-number 2)
@@ -552,12 +547,12 @@ See @url{http://mathworld.wolfram.com/TangentNumber.html} for a definition.
 
 
 
+@margin-note{Wikipedia: @hyperlink["http://en.wikipedia.org/wiki/Partition_(number_theory)"]{Partition}}
 @defproc[(partition-count [n Natural]) natural?]{
   Returns the number of partitions of @racket[n].
   A partition of a positive integer @racket[n] is a way 
   of writing @racket[n] as a sum of positive integers.
   The number 3 has the partitions @math-style{1+1+1, 1+2, 3}.
-  See @url{http://en.wikipedia.org/wiki/Partition_(number_theory)}.
   @interaction[(require math racket)
                (partition-count 3)
                (partition-count 4)]