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Abstract
This note presents a short proof showing that no Euler Perfect Box (EPB) can arise under the natural integer conditions (a,b,c,d,e,f,g \in \mathbb{N}+). Beginning with the general case (a
Euler Perfect Box
17 May 2026, Version 4
Working Paper
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This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.
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Comment number 1, Peter M: Jul 16, 2026, 17:41
Peter M
Jul 16, 2026, 17:41
1
In Case A), you show that g^2 cannot equal (b+c)^2, but this does not mean that g^2 is not a perfect square. Consider the case (a,b,c,g) = (3,4,12,13). Then all of the steps in case A) apply, except the conclusion that g^2 is not a perfect square, because g is an integer. The mistake is that case A) does not address the facts that d and f must also be integers.