Lin Hsin Hsin Palindromic Concatenation 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 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 ∈ 𝒟

b = rev(a)

n = ⌊log₁₀ a⌋ + 1

a ∥ b = a · 10ⁿ + b ≡ 0 (mod 11)

Proof

Work in ℤ/11ℤ.
Since 10 ≡ −1 (mod 11), 10ᵏ ≡ (−1)ᵏ

Step 1 Reduce a mod 11:

a = Σᵢ dᵢ · 10ⁱ ≡ Σᵢ dᵢ · (−1)ⁱ (mod 11) … (1)

Step 2 Reduce b mod 11:

b = Σᵢ dᵢ · 10ⁿ⁻¹⁻ⁱ ≡ (−1)ⁿ⁻¹ Σᵢ dᵢ · (−1)ⁱ ≡ (−1)ⁿ⁻¹ · a (mod 11) … (2)

Step 3 Compute the concatenation:

a · 10ⁿ + b ≡ a(−1)ⁿ + (−1)ⁿ⁻¹ · a = a[(−1)ⁿ + (−1)ⁿ⁻¹] = 0 (mod 11) ∎

Corollary

The quotient (a ∥ b) / 11 is a positive integer ∀ a ∈ 𝒟,
and the domain is unbounded above.

Examples

a	b = rev(a)	a ∥ b	= 11 ×
12	21	1221	111
56	65	5665	515
123	321	123321	11211
1198	8911	11988911	1089901