Uploaded September 2020 | Updated September 2026, 1 week ago
Proof that all powers of primitive roots are incongruent: youtu.be/TfZ9nPfOhQ0
The index of a number relative to a primitive root mod p is useful when considering things like quadratic residues. Here we define the idea of an index and give some basic properties and examples.
Quadratic Residues playlist: youtube.com/playlist?list=PLug5ZIRrShJGJieICD2KnqU9cRioaEBjB
0:00 Definition
1:04 log notation
2:17 Index of a product
4:51 Index of a power
5:57 Examples
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Music: OcularNebula - The Lopez
Proof that all powers of primitive roots are incongruent: youtu.be/TfZ9nPfOhQ0
The index of a number relative to a primitive root mod p is useful when considering things like quadratic residues. Here we define the idea of an index and give some basic properties and examples.
Quadratic Residues playlist: youtube.com/playlist?list=PLug5ZIRrShJGJieICD2KnqU9cRioaEBjB
0:00 Definition
1:04 log notation
2:17 Index of a product
4:51 Index of a power
5:57 Examples
Subscribe to see more new math videos!
Music: OcularNebula - The Lopez









![Functions as Sums of Exponentials
The 5 by 5 inverse matrix to play around with:
[ 1, -10, 35, -50, 24;
0, -1/6, 3/2, -13/3, 4;
0, 8, -64, 152, -96;
0, -81/2, 567/2, -567, 324;
0, 128/3, -256, 1408/3, -256 ]
A method to represent functions as a sum of exponentials. Use the inverse matrix and try it out on some functions to see what happens!
This video is a response to Dr. Peyams video about diagonalizing the differential operator.
New math videos every Monday and Friday. Subscribe to make sure you see them! Functions as Sums of Exponentials](https://i.ytimg.com/vi/lldiTpV6gX8/mqdefault.jpg)
