Beal Conjecture Explorer

Searching for counterexamples to A^x + B^y = C^z

Overview

The Beal Conjecture Explorer searches for counterexamples to the Beal Conjecture, which is a generalization of Fermat's Last Theorem. All power calculations are performed using Romasm assembly.

The Beal Conjecture

What is it?

The Beal Conjecture states that if:

A^x + B^y = C^z

where A, B, C, x, y, z are positive integers with x, y, z > 2, then A, B, and C must have a common prime factor.

Status: Unproven. A prize of $1 million is offered for a proof or counterexample.

Note: If A, B, C share a common factor, solutions exist (e.g., 2³ + 2³ = 2⁴).

Romasm Implementation

The explorer uses Romasm assembly to calculate powers and search for solutions:

; Check if A^x + B^y = C^z
; Uses stdlib power function
; Input: R0 = A, R1 = x, R2 = B, R3 = y

; Calculate A^x
LOAD R4, R0
LOAD R5, R1
CALL power      ; R0 = A^x

; Calculate B^y
LOAD R4, R2
LOAD R5, R3
CALL power      ; R0 = B^y
LOAD R6, R0     ; Store B^y in R6

; Add them
LOAD R0, R4     ; R0 = A^x
ADD R0, R6      ; R0 = A^x + B^y

; Now search for C^z that equals this value
; (Simplified - actual implementation searches systematically)

Using the Explorer

  1. Enter values for A, B, x, y (or let it search automatically)
  2. Click "Search for Counterexample"
  3. View any solutions found
  4. Check if A, B, C share a common factor

Related Documentation