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Hanoi mathematical society

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  • Hanoi Mathematical Society Hanoi Open Mathematical Olympiad 2010 Junior Section Sunday, 28 March 2010 08h45-11h45 Important: Answer all 10 questions. Enter your answers on the answer sheet provided. For the multiple choice questions, enter only the letters (A, B, C, D or E) corresponding to the correct answers in the answer sheet. No calculators are allowed.

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  • Hanoi Mathematical Society Hanoi Open Mathematical Olympiad 2010 Senior Section Sunday, 28 March 2010 08h45-11h45 Important: Answer all 10 questions. Enter your answers on the answer sheet provided. For the multiple choice questions, enter only the letters (A, B, C, D or E) corresponding to the correct answers in the answer sheet. No calculators are allowed. Q1. The number of integers n ∈ [2000, 2010] such that 22n + 2n + 5 is divisible by 7, is (A): 0; (B): 1; (C): 2; (D): 3; (E) None of the above. Q2. The last 5 digits of the number 52010 are (A): 65625; (B):...

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  • Hanoi Open Mathematical Olympiad 2006 Junior Section, Sunday, 9 April 2006 Q1. What is the last two digits of the number (11 + 12 + 13 + · · · + 2006)2 ? Q2. Find the last two digits of the sum 200511 + 200512 + · · · + 20052006 . Q3. Find the number of different positive integer triples (x, y, z) satisfying the equations x2 + y − z = 100 and x + y 2 − z = 124. Q4. Suppose x and y are two real numbers such that x + y − xy = 155 Find...

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