Erdős–Straus conjecture

The number-theoretic Erdős - Straus conjecture (after the mathematicians Paul Erdős and Ernst Gabor Straus ) states that always corresponds to a sum of three unit fractions.

The assumption

The equation has for every natural a solution, where, and also are natural numbers.

Geometric interpretation

The geometric interpretation of the Erdős - Straus conjecture provides for every natural a cuboid with edge lengths, and (, and natural numbers), so that its 8- fold volume divided by its surface gives the value of units of length.

Examples, remarks

• Two solutions are.

• For anyone a solution was found.

• For all natural with the assertion is trivial, since

• Even the somewhat more general case with natural is very easy to solve with and, because.

Mini - Erdős - Straus conjecture

A variant of the Erdős - Straus conjecture is the mini - Erdős - Straus conjecture, stating that to the equation for every natural a solution with natural and exists.

This assumption is incorrect because the equation iff no solution for natural and exists when all prime factors are of the form.

• Number Theory
• Conjecture ( mathematics)