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Imaginer1

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In summary, the conversation discusses the desire to prove mathematical statements at an intermediate level for practice. Some suggested problems include proving the sum of odd numbers is always a perfect square, finding a five-digit number where the third power of the first two digits is the entire number, and classifying all natural numbers x and y such that x^2-y^2=17. The conversation also suggests getting a textbook on basic number theory and recommends some exercises from a number theory course, such as proving that the greatest common divisor of two consecutive Fibonacci numbers is always 1 and that the product of an even number and an odd number is always even.

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Imaginer1

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Physics news on Phys.org

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2) Find a five digit number such that the third power of the first two digits is the entire number. So find abcde such that (ab)

3) Classify all natura numbers x,y such that [itex]x^2-y^2=17[/itex]. Generalize.

4) Not number theory and not easy, but very nice: Take a perfect n-gon in the unit circle. Take a special point x of the n-gon. Connect all other points of the n-gon with x. Prove that the length of all line segments is n.

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Imaginer1

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Yes.

Those seem exceedingly entertaining.

I SHALL BEGIN.

Those seem exceedingly entertaining.

I SHALL BEGIN.

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checkitagain

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There are four difficulty levels of exercises with hidden solutions.

Many are number theory type with other math subject area problems.

- #5

morphism

Science Advisor

Homework Helper

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I suppose what you meant to say here is: Take a perfect n-gon with its vertices on the unit circle. Take a special vertex x. Connect all other vertices to x. Prove that themicromass said:4) Not number theory and not easy, but very nice: Take a perfect n-gon in the unit circle. Take a special point x of the n-gon. Connect all other points of the n-gon with x. Prove that the length of all line segments is n.

Right?

re Imaginer1: Have you thought about getting a textbook on basic number theory? There are plenty of good ones that have lots of fun exercises.

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morphism said:I suppose what you meant to say here is: Take a perfect n-gon with its vertices on the unit circle. Take a special vertex x. Connect all other vertices to x. Prove that theproductof the lengths of the all line segments is n.

Yes, of course, thank you!

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Imaginer1

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re Imaginer1: Have you thought about getting a textbook on basic number theory? There are plenty of good ones that have lots of fun exercises.

I've thought about it, but haven't. Don't assume, however, that implies my knowledge on number theory doesn't stack up- actually, I'm currently working with the Mertens function growth rate, but that's a bit beyond the point.

- #8

Frogeyedpeas

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You might like the AoPS book-line just google that acronym and check out the website

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Frogeyedpeas

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20Tauri

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A selection of things to try proving, cribbed from my memory of number theory assignments:

Prove that for natural numbers x, y, z and prime p, x^p +y^p =z^p implies p divides x+y-z.

Prove that the greatest common divisor of two consecutive Fibonacci numbers is always 1.

Prove that the product of an even number and an odd number is always even.

For integers a and b and prime p, show that if a and b are both quadratic residues modulo p, then the product ab is also a quadratic residue modulo p.

"Proofs and puzzles for beginning mathematicians" is a book that introduces basic mathematical concepts and techniques through a series of puzzles and problems. It aims to develop critical thinking and problem-solving skills in young mathematicians.

This book is intended for beginning mathematicians, typically students in middle school or early high school. It can also be a helpful resource for anyone interested in developing their mathematical reasoning abilities.

The book covers a range of topics including logic, number theory, geometry, and algebra. It also includes puzzles and problems related to these topics to help reinforce the concepts.

No, this book is designed for readers with little to no prior knowledge in mathematics. It starts with basic concepts and gradually builds upon them, making it accessible for beginners.

This book uses puzzles and problems as a way to teach mathematical concepts, making it more engaging and interactive for young readers. It also includes solutions and explanations for each problem, allowing readers to check their work and understand the reasoning behind each solution.

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