The Hidden Structure of the Euro System
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Published June 11, 2026
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The Hidden Structure of the Euro System
Authors/Creators
el Issaoui, Bilal
Description
This paper identifies a hidden mathematical structure in the euro system. It shows that the fifteen denominations across five layers satisfy a linear Diophantine system N = pA + qB + rC + sD + tE with parameters (19, 9, 3, 3, 1) , and that the conditions p ≡ 1 (mod q) and t | s | r | q guarantee a single law: A₀ = dr(N) . The digital root is the compass of every valid denomination construction, computable in one step for any amount.
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N = pA + qB + rC + sD + tE with (p, q, r, s, t) = (19, 9, 3, 3, 1).
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Keywords
Number theory · Linear Diophantine systems · Digital root · Modular arithmetic · Currency systems · Denomination decomposition · A₀ = dr(N) · Combinatorics
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DOI
10.5281/zenodo.20635198
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[](https://doi.org/10.5281/zenodo.20635198)
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Resource type<br>Other
Publisher<br>Zenodo
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English
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Creative Commons Attribution 4.0 International
The Creative Commons Attribution license allows re-distribution and re-use of a licensed work on the condition that the creator is appropriately credited.
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Copyright
Copyright (C) 2026 Bilal El Issaoui
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Created
June 11, 2026
Modified
June 11, 2026
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