Mathematical olympiad treasures
International Mathematical Olympiad 2011 - IMC2011 day 2 ppt
... introduce 2n−1 f (k) < n f (n) ≤ 1/n2 g(n) = k=n Then g(n) − g(n + 1) = f (n) − f (2n) − f (2n + 1) = (f (2n) + f (2n + 1))3 − f (2n) − f (2n + 1) = (f (2n) + f (2n + 1)) f (2n) f (2n + 1) = ... |M \ A| + |F \ A| + |A| = 2( n − l) + l = 2n − l But the degree of any vertex of G is 2k and thus we get 2k ≤ 2n − l, that is, l ≤ 2n − 2k Finally, 2k − n < l ≤ 2n − 2k implies that k < 3n This ... f...
Ngày tải lên: 07/03/2014, 07:20
Hanoi Open Mathematical Olympiad - Problems and solutions pdf
... Questions of Hanoi Open Mathematical Olympiad 1.1 Hanoi Open Mathematical Olympiad 2006 1.1.1 Junior Section, Sunday, April 2006 1.1.2 Senior Section, Sunday, April 2006 1.2 Hanoi Open Mathematical ... = abcd be the 4-digit prime number Prove that the equation ax3 + bx2 + cx + d = has no rational roots 10 1.3 Hanoi Open Mathematical Olympiad 2008 1.3 Hanoi Op...
Ngày tải lên: 07/03/2014, 19:20
Toán học quốc tế olympiad vol6 lecture notes on mathematical olympiad courses for junior section vol 1
... k(k + 2) 1 − k k+2 for any positive integer k, so 1 1 1 + + + + + 15 35 63 99 14 3 1 1 1 + + + + + = × 3 × 5 × 7 × 9 × 11 11 × 13 1 1 1 = − + − + ··· + − 3 11 13 1 = × 1 = 13 13 Example 10 If ab ... 3x 5x − (1 + 3x) 15 − 2x + 16 − 2x =1 = = , 1 15 15 15 10 − 6x x 14 x − (10 − 6x) 10 − 13 x x 2x − − = − = , 2 14 14 x− it follows that 16 − 2x 10 − 13...
Ngày tải lên: 11/03/2014, 16:55
Junior Balkan Mathematical Olympiad 2016
... (a, b, c) such that the number N= (a − b)(b − c)(c − a) +2 is a power of 2016 (A power of 2016 is an integer of the form 2016n , where n is a non-negative integer.) Solution Let a, b, c be integers ... positive integer such that (a − b)(b − c)(c − a) + = · 2016n We set a − b = −x, b − c = −y and we rewrite the equation as xy(x + y) + = · 2016n (1) If n > 0, then the right hand side is div...
Ngày tải lên: 03/08/2016, 08:32
Hanoi open mathematical olympiad 2009
... What we love to we find time to do! Nguyen Anh Hanoi Mathematical Society Tuan Hanoi Open Mathematical Olympiad 2009 Senior Section Sunday, 29 March 2009 08h45 - 11h45 Important: Answer all 14 questions ... allowed Q1 What is the last two digits of the number 1000.1001 + 1001.1002 + 1002.1003 + … + 2008 .2009? (A) 25; (B) 41; (C) 36; (D) 54; (E) None of the above Q2 Which is l...
Ngày tải lên: 03/12/2016, 05:12
43 rd International Chemistry Olympiad
... Calculate the standard potential for the cathode half reaction if the standard reduction potential for the anode half reaction is 0.83 V and fG (H2O(l)) is -237 kJ·mol-1 4 3rd IChO Theoretical ... = as v = at K E = 2(Eo + E = - (Eo + 1546 ) - (Eo + )= - + 8167 )) = 0.0 1435 (HD) = 4 3rd IChO Theoretical Problems, Official English Version Name: Code: · = · = 1.1154 10 =...
Ngày tải lên: 29/06/2013, 19:58
Nitrogen Dynamics and Biomass Production in a Vertical Flow Constructed Wetland Cultivated with Forage Rice and their Mathematical Modeling
... the leaf area Roughly, the plant height increased until 120 days after transplantation, and thereafter a constant height was maintained in every case The leaf area index (LAI), however, increased ... with forage rice is a fascinating subject To design an adequate VF constructed wetland using forage rice, it is required to understand in detail the dynamics of nutrients...
Ngày tải lên: 05/09/2013, 09:38
Optimization of design and operating parameters on the year round performance of a multi-stage evacuated solar desalination system using transient mathematical analysis
... performance and thermal characteristics of the system Description of the multi-stage evacuated solar desalination system The Multi-stage evacuated solar desalination system is a combination of ... Results and discussion There are many design and operating parameters which affect the performance characteristics and distillate yield of...
Ngày tải lên: 05/09/2013, 16:11
