lean_workbook_plus_46052

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Disproved status carries no information about that problem. Do not import this node or use it as a dependency.

Now note that all the powers of $10$ are odd, hence $\equiv -1\pmod{11}$ , and also $123456789\equiv -1-1-1-1+9\equiv 5\pmod{11}$ . Therefore $N\equiv 1-(99+98+\dots +10)-5\equiv 1-{99+10\over 2}\cdot 90-5\equiv 1-109\cdot 45-5\pmod{11}$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_46052 :
  (123456789 * 10^10 - 99 * 10^9 - 98 * 10^8 - 97 * 10^7 - 96 * 10^6 - 95 * 10^5 - 94 * 10^4 - 93 * 10^3 - 92 * 10^2 - 91 * 10 - 90) % 11 = 5   :=  by sorry

The target invents a different finite polynomial with consecutive exponents; the excerpt only specifies a modular calculation for an absent N.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

Restore the actual definition of N and its odd-exponent decimal blocks before evaluating the congruence.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.