# Browse Classroom Capsules and Notes

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Displaying 51 - 60 of 133

The author gives a new formulation of the conjecture.

Goldbach's conjecture on the expression of odd numbers and some examples

A simple proof for Last Fermat Theorem when n=4 in Gaussian Integers

A simple geometric proof for the formula $1 + 3 + 5 + \ldots + (2n - 1) + (2n + 1) + (2n - 1) + \ldots + 5 + 3 + 1 = n^2 + (n + 1)^2$

The graph obtained by constructing an edge between each pair of primes with difference a power of 2 is not connected.

An interesting unusual visual and rigorous proof of Fermat`s Little Theorem, with unusual generalizations

If two elements in a ring are multiples of each other, are they necessarily unit multiples? In general, the answer is no; it is yes for the integers mod $n$.
The author constructs infinitely many integer solutions to the title equation $X^n + Y^n = Z^{n+1}$.