[Maple] Frequencia 2012

equivale := proc (p, q) options operator, arrow; (not p or q) and (p or not q) end proc;
(p, q) -> (not p or q) and (p or not q)
for p in [true, false] do for q in [true, false] do print(p, q, equivale(p, q)) end do end do;
                        true, true, true
                       true, false, false
                       false, true, false
                       false, false, true
X := {seq(x, x = 1 .. 7)};
                     {1, 2, 3, 4, 5, 6, 7}
for x in X do for y in X do if irem(x^3*y+x*y^3, 5) <> 2 then print(x, y) end if end do end do;
                              1, 2
                              1, 3
                              1, 4
                              1, 5
                              1, 7
                              2, 1
                              2, 3
                              2, 4
                              2, 5
                              2, 6
                              3, 1
                              3, 2
                              3, 4
                              3, 5
                              3, 6
                              3, 7
                              4, 1
                              4, 2
                              4, 3
                              4, 5
                              4, 6
                              4, 7
                              5, 1
                              5, 2
                              5, 3
                              5, 4
                              5, 5
                              5, 6
                              5, 7
                              6, 2
                              6, 3
                              6, 4
                              6, 5
                              6, 7
                              7, 1
                              7, 3
                              7, 4
                              7, 5
                              7, 6
for x in X do for y in X do if irem(x^3*y+x*y^3, 5) = 2 then print(x, y); break; break end if end do end do;
                              1, 1
                              2, 2
                              3, 3
                              4, 4
                              6, 1
                              7, 2

Y := {seq(y, y = 0 .. 10)};
               {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
for x in Y do for y in Y do if (x+1)^2+y^2 = 100 then print([x, y]) end if end do end do;
                             [5, 8]
                             [7, 6]
                             [9, 0]
h := proc (n) options operator, arrow; piecewise(n < 5, 1, 5 <= n, sum(j/(j+1), j = 1 .. n)) end proc;
              /                    n        \
              |                  -----      |
              |                   \         |
              |                    )     j  |
n -> piecewise|n < 5, 1, 5 <= n,  /    -----|
              |                  ----- j + 1|
              \                  j = 1      /
evalf(h(8));
                          6.171031746
f := proc (n) options operator, arrow; piecewise(n = 1, 1, 2 <= n, (1/2)*n*f(n-1)) end proc;
              /                  1           \
n -> piecewise|n = 1, 1, 2 <= n, - n f(n - 1)|
              \                  2           /
f(20);
                         9280784638125
                         -------------
                               2
evalf(%);
                                      12
                        4.640392319 10
for n to 10 do if irem(f(n), 2) = 0 then print(n) end if end do;
Error, invalid input: irem received 3/2, which is not valid for its 1st argument, m