1. page 12 problem 33: replace "100" by "99"

2. page 126 line 3: replace "f(U)\subset V" by "f(U)\backslash\{x_0\})\subset V"

3. Page 303 line 15: replace the display by 1\leq c_0\leq b_1< c_1< b_2< \cdots < b_i

4. Page 303 line 17: replace "E\subset A" by "E=A\cap (\{1,2,\ldots, n\}\backslash \{c_0,b_1,c_1,b_2,\ldots, b_m,c_m\})"

5. Page 405 line 9 from the bottom: repalce "\mbox{Re}(-a_2z^{-2}-\cdots -a_nz^{-n})" by "\mbox{Re}(-a_{n-2}z^{-2}-\cdots -a_0z^{-n})"

6. Page 406 line 8 from the bottom: add "\leq 9(|z|^{-2}+|z|^{-3}+\cdots +|z|^{-n})" at the begining of the line in the second line of the display.

7. Page 263 line 5: replace "4^1+1^2" by "4^1+1^2+1" (add a 1)

8. Page 324 line 21: replace "S_n" by "S_9"

9. page 294 problem 856: replace the second occurence of the word "edges" by "vertices"

10. page 292 first line: after "complete graph" add " with $R(p,q)$ vertices"

11. page 515 line 15: insert "Mathematical" between "Romanian" and "Olympiad"

12. page 68 line 5 from the bottom: replace "positive" by "nonnegative"

13. page 79 line 4 from the bottom: delete the comma between "mechanics" and "observable"

14. page 296 line 4 from the bottom: insert "of" between "and" and "the position"

15. page 312 line 10: delete the word "combinatorial"

16. page 132 line 15: - delete the bar over z in $\psi(z)=f(z)-f(-\bar{z})$ - on next line, delete the entire content of the paranthesis; the phrase should end with the word "continuous" - on next line delete the bar over z_0 - in the display, delete the two bars over z_0 To conclude, in the entire paragraph there should be no bars.

17. page 148 lines 8 and 6 from the bottom: to be very rigorous, the argument of the natural logarithm in the two displays should be taken in absolute value. So we should have "\ln |\sin x+\cos x|" instead of "\ln (\sin x+\cos x)", three times.

18. page 103 line 9: the two exponents in the general term formula should both be $n$, not $m$.

19. Replace the first example from section 2.2.3. page 52 with the following:
\begin{example}
Find all cubic polynomials $P(x)$ with the property that $P(x)$ is a multiple of $P''(x)$.
\end{example}

\bes
Set $P(x)=Q(x)P''(x)$, with $Q(x)$ a quadratic polynomial. Differentiation twice this relation we obtain
\begin{eqnarray*}
P''(x)=Q''(x)P''(x)+Q'(x)P'''(x).
\end{eqnarray*}
Hence $P''(x)(1-Q''(x))=Q'(x)P'''(x)$. We deduce that $P'(x)$ is a constant multiple of $Q'(x)$. Incorporating the constant into $Q(x)$, we see that $P(x)=Q(x)Q'(x)$ for some quadratic polynomial $Q(x)$. It is not hard to check that each polynomial of this form has the desired property.
\ens

20. Page 718 line 1: 7^z should be 7^zx

21. On the back cover there is a repeated "to" on the last line.

22. Page 7 line 1: add "a" before $1\times 1$.

23. Page 93 line 21: in the statement of problem 286 it would look much better if instead of "$(\sin n)_n$" there was "$(\sin n)_{n\geq 1}$"

24. Page 183 last line: replace {\bf i} {\bf j} {\bf k} by \vec{i} \vec{j} \vec{k}

25. Page 102 line 9: replace "$\lambda _{1,2}=\frac{1\pm \sqrt{5}}{2}$" by "$\lambda _1=\frac{1-\sqrt{5}}{2}$ and $\lambda_2=\frac{1+\sqrt{5}}{2}$"

26. Page 206 line 11: "Let $ABC$ be a convex quadrilateral" should be "Let $ABCD$ be a convex quadrilateral"

27. Page 254 line 15: put ( ) around f(2n+1) and f(2n) so that they look like (f(2n+1))^2-(f(2n))^2

28. Page 585 line 11: insert "not" between "is" and "identically"

29. Page 684 line 13: "\lfloor x_1+\frac{1}{2}\rfloor" should read "\lfloor nx_1+\frac{1}{2}\rfloor" an n is missing

30. Page 185 line 4 from the bottom: the third term in the equation should be "\frac{(x+f(0))^2-(x-y)^2-(f(0))^2+y^2}{2x}"

31. Page 112 line 4 from the bottom: replace "\frac{1}{2}(x+1)" and "2(x+1)" by "\frac{1}{2}(x+2)" and "2(x+2)"

32. Page 112 line 2 from the bottom : replace "x\cdot \frac{x+1}{2}" by "x\cdot \frac{x+2}{2}" and "2x(x+1)" by "2x(x+2)"

33. Page 331 line 7: Delete the sentence that starts with "We assume in" and ends with "problem."

34. Page 610 line 4 from the bottom: the vertical bars around the cross product of OM and OP should be doubled, therefore they should be \| and \|

35. Page 610 line 1 from the bottom: in the bracket, the \times between AE and AC should be +

36. Page 199 delete lines 13 and 14, namely delete the sentence that starts with "An alternative approach..."

37. Page 730 line 4 from the bottom: delete the comma between $r-1$ and transpositions.

38. Page 547 line 4 from the bottom: it should be $f'(x)\geq f'(1)$

39. Page 159 line 13: replace $f'(0)>0$ by $f'(1)>0$.

40. The solution to problem 818 at page 279 is wrong and cannot be fixed. Here is a possible replacement:
Find all positive integers $x,y$ such that $15^x-6^y=9$.

Solution (to be replaced at page 722, line 4):
Clearly $x=y=1$ is a solution, while $y=2$ does not yield a solution. If $y>2$, then reducing modulo $4$ we obtain that $x$ is even, $x=2n$. The equation can be rewritten as $15^{2n}-9=6^y$ or
\begin{eqnarray*}
9(5^n\cdot 3^{n-1}+1)(5^n\cdot 3^{n-1}-1)=2^y\cdot 3^y.
\end{eqnarray*}
Because $y>2$, the left-hand side should have an additional factor of $3$. This can only happen when $n=1$, so the only other solution to the given Diophantine equation is $x=2,y=3$.

41. Page 304 problem 882: in the first sum, the summation should be from "i=0" instead of "j=0"

42. Page 761 line 12: $\{0,1\}^n$ should be $\{0,1\}^{p+q+1}$.

43. Page 760 line 9: the expression in the display should be $\sum_{k=0}^m{m\choose k}{{n+k}\choose m}$. The expression written there has nothing to do with the problem.

44. Page 30 line 13: in the display there should be $(n-1)^2$ instead of $(n^2-1)^2$.

45. Page 41: problem 122 is silly, it should be ignored.

46. Page 268 line 2 from the bottom: the $a_n$ in $x\equiv a_n$ should be $a_k$.

47. Page 269 line 8: Warsawa should read Warszawa.

48. Page 711 line 7 from the bottom: Warsawa should read Warszawa.

49. Page 132 in the solution to the example, all the bars over z and z_0 should be ignored (there are 5 of them). As such, "$-z$ is diametrically opposite to $z$".

50. Page 480 the third display: the "+4" in the denominator should be a "+2".

51. Page 255 line 12: the union of sets should be intersection of sets (because of de Morgan's law).

52. Page 373 line 9 from the bottom: In the display, there is an extra bracket in the term |\epsilon(z-\epsilon)|; delete it.

53. Page 330 line 2: replace "x_j>0, x_{j+1}<0", and "x_j+x_{j+1}" by "x_j>0, x_{j+1}\leq 0". The original condition is too strong (e.g 2,3,-4) and not needed.

54. Page 324 lines 3, 5, 6: replace "16" by "15".

55. page 323 line 4 from the bottom: while the solution is not incorrect as is, the number 29 can be replaced by 27 in the argument, namely 21 plus the 6 numbers that can have repeated prime factors.

56. page 84 line 2 from the bottom: replace $n$-dimensional sphere by $n-1$-dimensional sphere.

57. page 86 line 18: replace $K_0$ by $K_1$.

58. page 86 line 19: replace $K$ by $K_1$.

59. page 424 line 12: in the last sum there should be a cosine before $k(m+j)\alpha$.

60. page 555: The solution to problem 497 is wrong. I think the following fix works. Replace replace everything starting with the second line at the bottom of page 555 to the second equation on top of page 556 by
" Similarly
\begin{eqnarray*}
(-1)^m\int_0^\pi f^{(2m)}(x)(n\sin x+sin nx)dx =(na_1-n^{2m}a_n)\frac{\pi}{2}\geq 0.
\end{eqnarray*}"

61. page 239 line 12: in the expression on the left-hand side, the denominator of the first factor in the second term should be 2z not 2x.

62. page 351 line 2: "9/2" should read "13/2".

63. On the front cover of the book, on the last line of the design there is a parenthesis missing in "(x,y)"

64. page 41 line 7: the "2" in the parenthesis should be a "w"

65. page 100, in the determinant at the bottom of the page, on the first row of the determinant there is a "-" missing in front of "a_{k-1}"

66. This is not a typo, just a remark. The answer to problem 298 could also be written as "a_k = \lfloor{\frac{k}{2}}\rfloor^2 + \lceil{\frac{k}{2}}\rceil^2"

67. page 50, line 8 from the bottom: "m^3-3m^3+27m-20" should read "m^3-9m^2+27m-20"

68. page 53. lines 13, 14, 16: in all the summations, the "k" should be "n"

69. page 115, in the statement to problem 341, the condition should be "p\neq -1"

70. Another way to write the answer to problem 298 is "x_n = \lfloor{\frac{n}{2}}\rfloor^2 + \lceil{\frac{n}{2}}\rceil^2"

71. page 464 line 8 from the bottom, "u^n and \bar{u}^n" should read "u and \bar{u}"

72. page 464 line 4 from the bottom, S_2 should be "S_2=1-a"