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.
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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.