Learn · An Introduction to Number Theory
Lecture 37 of 48Week 10
Lecture 37: Congruent Numbers - I
Prof. Somnath Jha · IIT Kanpur
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- An Introduction to Number Theory, IIT Kanpur (at NPTEL)
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All the lectures
- Lecture 1: Abelian Groups - I
- Lecture2: Abelian Groups - II
- Lecture3: Abelian Groups - III
- Lecture 4: Abelian Groups - IV
- Lecture 5: Abelian Groups - V
- Lecture 6: Abelian Groups - VI
- Lecture 7: Commutative Rings - I
- Lecture 8: Commutative Rings - II
- Lecture 9: Commutative Rings -III
- Lecture 10: Chinese Reminder Theorem
- Lecture 11: Fermat's Little Theorem and Wilson's Theorem
- Lecture 12: Prime ideals and maximal ideals
- Lecture 13: Ideals in a PID
- Lecture 14: Ideals in a UFD
- Lecture 15: Gauss Lemma
- Lecture 16: Field Extensions
- Lecture 17: Finite Fields
- Lecture 18: Multiplicative groups of finite fields
- Lecture 19: Legendre Symbol
- Lecture 20: Quadratic Reciprocity
- Lecture 21: Zero sets of polynomials
- Lecture 22 : Ring of quadratic integers - I
- Lecture 23 : Ring of quadratic integers - II
- Lecture 24 : Gaussian integers
- Lecture 25: Ring of quadratic integers - III
- Lecture 26 : Ring of quadratic integers - IV
- Lecture 27: Ideal class group of quadratic fields
- Lecture 28: Binary quadratic forms
- Lecture 29: Binary quadratic forms and ideal class group of imaginary quadratic fields – I
- Lecture 30: Binary quadratic forms and ideal class group of imaginary quadratic fields – II
- Lecture 31: Binary quadratic forms and ideal class group of imaginary quadratic fields – III
- Lecture 32: Binary quadratic forms and ideal class group of imaginary quadratic fields – IV
- Lecture 33: Units in the rings of quadratic integers
- Lecture 34: Integral solutions of the equation 𝑥 2 − 2𝑦 2 = 1
- Lecture 35: Dirichlet's approximation theorem
- Lecture 36: Brahmagupta - Pell's equation
- Lecture 37: Congruent Numbers - I
- Lecture 38: Congruent Numbers - II
- Lecture 39: The n = 4 case of the Fermat's Last Theorem
- Lecture 40: Congruent Numbers and Elliptic Curves
- Lecture 41: Sum of two squares theorem
- Lecture 42: Sum of four squares theorem
- Lecture 43: Sum of integer cubes
- Lecture 44: Rational cube sum problem
- Lecture 45: Affine and Projective Spaces- I
- Lecture 46: Affine and Projective Spaces- II
- Lecture 47: Elliptic Curves - I
- Lecture 48: Elliptic Curves - II