I need a book for math competitions

  • #1
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Hi
As the title suggests, I'm looking for a math book that has some competition-style problems in it, with explanations on how to solve them. I have found numerous of other competitions online but the explanations are very not understandable for me. I am NOT talking about international competitions, but regional. This is high school math.

Here is an example:

Find all prime numbers p and q and a natural number r such that they satisfy the equation.

p2 + q2+pq = r2
 

Answers and Replies

  • #2
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You might find recreational mathematics books with a focus on puzzles useful. My Best Mathematical and Logic Puzzles by Martin Gardner, for example.
 
  • #3
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I checked the book and I think I should add another example for better understanding.

Determine a maximum and a minimum of the function:

f(x)=√(sin4(x)+4cos2(x)) - √(cos4(x) + 4sin2(x))
 
  • #4
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If you want to learn background knowledge, challenging problems along with good explanations, I recommend any book written by Titu Andreescu.
 
  • #5
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"104 Number Theory Problems: From the Training of the USA IMO Team," "Schaum's 3,000 Solved Problems in Calculus," and "Challenging Problems in Algebra" might help you, then.
 
  • #6
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"104 Number Theory Problems: From the Training of the USA IMO Team," "Schaum's 3,000 Solved Problems in Calculus," and "Challenging Problems in Algebra" might help you, then.
Thumbs up for "104 NT Problems"; I used it to learn basics of elementary NT before studying analytics aspect. I think that book can be used as a first introduction to ENT too. Any book by Andreescu is extremely well-written.
 
  • #7
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"104 Number Theory Problems: From the Training of the USA IMO Team," "Schaum's 3,000 Solved Problems in Calculus," and "Challenging Problems in Algebra" might help you, then.
I found the last book, and it is perfect, thank you
 
  • #8
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I have found an interest in problem solving myself. I ordered, but have yet to receive and view the contents of, two books. One is the USSR Olympiad Math problems book published by Dover and a problems book published by the MAA.
 
  • #9
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I have found an interest in problem solving myself. I ordered, but have yet to receive and view the contents of, two books. One is the USSR Olympiad Math problems book published by Dover and a problems book published by the MAA.
Thank you but I think it should be said. The problems I am solving are much easier than any olympiad problems.
 

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