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Euler Perfect Box

30 September 2024, Version 3
Working Paper
This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.

Abstract

1- I chose a box of different dimensions. H = a, W = a + r, L = a + k, and (k ≠ r ≠ a) Substitute in equation: g^2 =a^2 +b^2 +c^2, g ∈ N+ ⇒ a =r = k … contradiction to (k ≠ r ≠ a) If (k ≠ r ≠ a) ⇒ g ∉ N+ 2- If W = L, or W = L = H ⇒ d (diagonal) ∉ N+ ∴ from all above the Euler Perfect Box doesn’t exist.

Keywords

Euler
Perfect Box
Math
Unsolved Math
Taha
UK
USA
Kurdistan

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Version History

Sep 30, 2024 Version 3

Version Notes

If a, b, c, d, e, f ∈N_+, and if g ∈ N_(+ ) too, then Euler Perfect Box exist LHS of eq3:-3(3^2)-2(3)(5) = -57 RHS of eq3: 2(3)4 + 4^2 -2(3)5-3^2 = 1 LHS of eq3:-3(6^2)-2(6) (5) = -168 RHS of eq3: 2(6)4 + 4^2 -2(6)5-6^2=-32

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License

All Rights Reserved

DOI

10.33774/coe-2024-47ld9-v3
D O I: 10.33774/coe-2024-47ld9-v3 [opens in a new tab]

Author’s competing interest statement

The author(s) have declared they have no conflict of interest with regard to this content

Ethics

The author(s) have declared ethics committee/IRB approval is not relevant to this content

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