Lin Hsin Hsin Palindromic Concatenation Sum Theorem & Proof from the founder of LIN HSIN HSIN ART MUSEUM--Digital Art Museum, First Virtual Museum in the World, 1994.Wikipedia, Digital Media Center: Technology, Digital Art, Digital Paintings, Digital Sculptures, Digital Music, Digital Musical Instruments, Sound, Poetry, Animated Music, Web-enabled, Interactive, Digital Media Poineer

Lin Hsin Hsin
Artificial Intelligence Center
Sep 16, 2026, 08:15 SGT declares Lin Hsin Hsin Palindromic Concatenation Sum Theorem & Proof

Definitions

Definition 1

(Digit Reversal)

a ∈ ℕ

a = d_n−1 d_n−2 ⋯ d₁ d₀

n ≥ 2

d_n−1 ≥ 1

d_i ∈ {0,…,9}

rev(a) = d₀ d₁ ⋯ d_n−2 d_n−1

Definition 2

(Concatenation)

a, b ∈ ℕ

a ∥ b := a · 10ⁿ + b

Definition 3

(Domain)

𝒟 := { a ∈ ℕ : a ≥ 11, rev(a) ≥ 11 }

Theorem

A, B, X, Y

N₁ = A‖B‖B‖A

N₂ = X‖Y‖Y‖X

N₁ + N₂

Proof

Step	Statement	Justification
1	N₁ is a palindrome with an even number of digits	By construction: A‖B‖B‖A
2	N₁ ≡ 0 (mod 11)	Even-digit palindrome ⇒ divisible by 11
3	N₂ is a palindrome with an even number of digits	By construction: X‖Y‖Y‖X
4	N₂ ≡ 0 (mod 11)	Even-digit palindrome ⇒ divisible by 11
5	N₁ + N₂ ≡ 0 + 0 ≡ 0 (mod 11)	Congruence addition

N₁ + N₂

Examples

A="13", B="3" → N₁ = 133331 | X="55", Y="6" → N₂ = 556655
N₁ + N₂ = 133331 + 556655 = 689986
689986 ÷ 11 = 62726 ✓