Erdos-Straus Conjecture Explorer

Finding unit fraction decompositions of 4/n

Overview

The Erdos-Straus Conjecture Explorer searches for solutions to the unit fraction decomposition problem: expressing 4/n as the sum of three unit fractions (1/x + 1/y + 1/z). All computations are performed using Romasm assembly.

The Erdos-Straus Conjecture

What is it?

The Erdos-Straus Conjecture states that for every integer n ≥ 2, there exist positive integers x, y, z such that:

4/n = 1/x + 1/y + 1/z

Examples:

  • 4/2 = 1/1 + 1/2 + 1/2
  • 4/3 = 1/2 + 1/3 + 1/6
  • 4/5 = 1/2 + 1/4 + 1/20
  • 4/7 = 1/2 + 1/15 + 1/210

Status: Verified up to very large numbers, but unproven for all n.

Romasm Implementation

The explorer uses Romasm assembly to search for solutions:

; Find unit fraction decomposition for 4/n
; Input: R0 = n
; Output: R1, R2, R3 = x, y, z (if solution found)

LOAD R1, 1        ; Start with x = 1
LOAD R4, 4        ; Constant 4
LOAD R5, 1        ; Constant 1

search_loop:
  ; Try different values of x, y, z
  ; Calculate 1/x + 1/y + 1/z
  ; Compare with 4/n
  
  ; (Simplified - actual implementation is more complex)
  ; Uses fraction arithmetic in Romasm
  
  INC R1
  CMP R1, R0
  JLT search_loop
  
  ; If solution found, return x, y, z
  RET

Using the Explorer

  1. Enter a value for n (≥ 2)
  2. Click "Find Decomposition"
  3. View all possible solutions (x, y, z)
  4. See the verification that 1/x + 1/y + 1/z = 4/n

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