I need a book for math competitions

[Zeroth]

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

 

[The Bill]

You might find recreational mathematics books with a focus on puzzles useful. My Best Mathematical and Logic Puzzles by Martin Gardner, for example.

 

[Zeroth]

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))

 

[bacte2013]

If you want to learn background knowledge, challenging problems along with good explanations, I recommend any book written by Titu Andreescu.

 

[The Bill]

"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.

 

[bacte2013]

"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.

 

[Zeroth]

"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

 

[MidgetDwarf]

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.

 

[Zeroth]

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.