A Pythagorean introduction to number theory : right triangles, sums of squares, and arithmetic /
512.7
Takloo-Bighash, Ramin,
A Pythagorean introduction to number theory : right triangles, sums of squares, and arithmetic / Ramin Takloo-Bighash. - 1 online resource. - - Undergraduate Texts in Mathematics, 0172-6056 . - Undergraduate texts in mathematics. .
Academic Part I Foundational Material -- 1. Introduction -- 2. Basic number theory -- 3. Integral solutions to the Pythagorean Equation -- 4. What integers are areas of right triangles? -- 5. What numbers are the edges of a right triangle? -- 6. Primes of the form 4k+1 -- 7. Gauss sums, Quadratic Reciprocity, and the Jacobi symbol -- Part II Advanced Topics -- 8. Counting Pythagorean triples modulo an integer -- 9. How many lattice points are there on a circle or a sphere? -- 10. What about geometry? -- 11. Another proof of the four squares theorem -- 12. Quadratic forms and sums of squares -- 13. How many Pythagorean triples are there? -- 14. How are rational points distributed, really? -- Part III Appendices -- A. Background -- B. Algebraic integers -- C. SageMath -- References -- Index.
Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time;
Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.
English
9783030026042 3030026043
10.1007/978-3-030-02604-2 doi
com.springer.onix.9783030026042 Springer Nature
GBB917602 bnb
Number theory., Pythagorean theorem., Number Theory., Number theory., Pythagorean theorem.,
Electronic books.
QA241 / .T35 2018
Takloo-Bighash, Ramin,
A Pythagorean introduction to number theory : right triangles, sums of squares, and arithmetic / Ramin Takloo-Bighash. - 1 online resource. - - Undergraduate Texts in Mathematics, 0172-6056 . - Undergraduate texts in mathematics. .
Academic Part I Foundational Material -- 1. Introduction -- 2. Basic number theory -- 3. Integral solutions to the Pythagorean Equation -- 4. What integers are areas of right triangles? -- 5. What numbers are the edges of a right triangle? -- 6. Primes of the form 4k+1 -- 7. Gauss sums, Quadratic Reciprocity, and the Jacobi symbol -- Part II Advanced Topics -- 8. Counting Pythagorean triples modulo an integer -- 9. How many lattice points are there on a circle or a sphere? -- 10. What about geometry? -- 11. Another proof of the four squares theorem -- 12. Quadratic forms and sums of squares -- 13. How many Pythagorean triples are there? -- 14. How are rational points distributed, really? -- Part III Appendices -- A. Background -- B. Algebraic integers -- C. SageMath -- References -- Index.
Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time;
Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.
English
9783030026042 3030026043
10.1007/978-3-030-02604-2 doi
com.springer.onix.9783030026042 Springer Nature
GBB917602 bnb
Number theory., Pythagorean theorem., Number Theory., Number theory., Pythagorean theorem.,
Electronic books.
QA241 / .T35 2018