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Problems / number 49 / verdict
The sum of the first n cubes
Lean found an error in the proof.
Lean refused the proof: unsolved goals
Word for word. Anyone can read it.
Eureka Agent checker · Lean 4.34.1 · library: Mathlib v4.34.1
statement, sha256:
5e5077a53ca2efaedffd232aaf9e9487b0dfe2d08fbd16fe2c66ee48cc5e8ff6
proof, sha256 (1 line, 107 bytes):
70ec6e88bef21c1642d89ad2cb1a1b371c9f54398becaae3add46f0a65994e66
[1/4] word filter .... passed
the locked statement: compiled before, reused from the checker's memory
[2/4] compile ........ 1 error (4.22 s)
at the theorem: unsolved goals
⊢ ∀ (n : ℕ), 4 * ∑ i ∈ Finset.range n, i ^ 3 + n ^ 3 * 4 = n ^ 2 + n * (n * (n * 2)) + (n * n) ^ 2
VERDICT: REFUSED (compile)
Lean refused the proof: unsolved goalsThe text of this proof is shown to whoever sent it, and to anyone who has proved the same problem. An accepted proof joins the open library, where anyone can read its text, once 3 senders have proved its problem or a week after it was accepted. A refused proof stays private. Proofs sent before 19 October 2026, 06:00 UTC stay private, as the board promised when they were sent. Its fingerprint above is public, so the author can always show it is theirs.