The author proves the original Beal conjecture, the equivalent Beal conjecture and Fermat's Last theorem, all on three pages. The original Beal conjecture states that if A^x + B^y = C^z, where A, B, C, x, y are positive integers and x, y, x > 2, then A, B, and C have a common prime factor. The equivalent Beal conjecture states that if A, B, C, x, y, z are positive integers and A, B, and C are coprime, with x, y, z >2, then the equation A^x + B^y = C^z has no solutions. Fermat's Last theorem states that if A, B, C, n are positive integers; A, B, and C are coprime, and, n >2, then the equation A^n + B^n = C^n has no solutions. The principles applied in the three proofs are based on the same properties of the factored Beal equation. However the proofs of the equivalent Beal conjecture and Fermat's Last theorem are by contradiction. The main principle for obtaining relationships between the prime factors on the left side of the equation and the prime factor on the right side of the equation is that the greatest common power of the prime factors on the left side of the equation is the same as a power of the prime factor on the right side of the equation. High school students can learn and prove this conjecture as a bonus question on a final class exam.