Professor Jay Jorgenson

Starting with modular arithmetic.

Ascii code for ≡ is 240. (Alt-240). No need Latex for this.

± is 241.

≥ is 242.

≤ is 243.

And I think I'll use % for mod. Simpler.

This not a blog nor devotional page, it is simply my diary or journal

Professor Jay Jorgenson

Starting with modular arithmetic.

Ascii code for ≡ is 240. (Alt-240). No need Latex for this.

± is 241.

≥ is 242.

≤ is 243.

And I think I'll use % for mod. Simpler.

On congruences:

I think this is right:

Expanding theorem 4.7, Rosen - Elementary number theory and its applications

Theorem: If a, k, and m are integers such that k > 0, m >0, and a ≡ 1 (mod m), then a^k ≡ a (mod m).

Proof: hint: let a = b + 1. It is obvious that m | b. This, (b+1)^k = b(b^(k-1) + ...) + 1, ...

Primes as Sums of Two Squares:

Such primes are in the form: 4n + 1

I would like to find a geometric proof of it.