User:Z423x5c6/add something

Zero and One are the only Consecutive Perfect Squares
(generalize?)

Complex Numbers as External Direct Product
(explain)

Category:Quaternion Modulus
(refer to Category:Complex Modulus)

Trigonometric Functions in terms of each other
(add something)

Grassmann's Identity
(try to create a proof using first isomorphism theorem)

Maximum Number of Steps taken by Euclidean Algorithm
(We need at most $5$ steps to reduce the number of digits by $1$, and some marginal cases to be handled. Have some difficulties to write it out rigorously...come back later...)