Sum of two squares, a power of 3, and a power of 5

formal-conjectures · oeis · ams-11

Any integer $n > 1$ can be written as $a^2 + b^2 + 3^c + 5^d$ where $a, b, c, d$ are
nonnegative integers.

Zhi-Wei Sun has offered a \$3,500 prize for the first proof.

**Zhi-Wei Sun's Conjecture (A303656)**: Any integer $n > 1$ can be written as the sum of two
squares, a power of 3, and a power of 5.

Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).

Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.

Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://oeis.org/A303656
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://arxiv.org/abs/1701.05868v10
Upstream reference cited by formal-conjectures (checked 2026-09-11): http://maths.nju.edu.cn/~zwsun/RefineFourSquareTh.pdf
Upstream reference cited by formal-conjectures (checked 2026-09-11): http://maths.nju.edu.cn/~zwsun/Square-sum.pdf
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://www.aimspress.com/aimspress-data/era/2020/2/PDF/1935-9179_2020_2_589.pdf
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/OEIS/303656.lean
Local target: Corpus.OEIS303656.conjecture
Source SHA-256: 92285034cae1339341f3413698a759ddf3abffccb01c32e09090b0254dbc4ce2
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.

Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.

Public JSON record