Changming Qiu

On the {0,1} Case of Guy's Problem F24: Reduction to a Pell‑Type Obstruction with Leading‑Digit Constraints

We study positive integers n such that the decimal expansion of n²,without leading zeros,uses only the digits 0 and 1.The known examples are the powers of 10.We prove a structural reduction to a Pell‑type family and a leading‑digit restriction to {1,3}.First,via a p‑adic valuatio...

On the {0,1} Case of Guy's Problem F24: Reduction to a Pell‑Type Obstruction with Leading‑Digit Constraints

We study positive integers n such that the decimal expansion of n²,without leading zeros,uses only the digits 0 and 1.The known examples are the powers of 10.We prove a structural reduction to a Pell‑type family and a leading‑digit restriction to {1,3}.First,via a p‑adic valuatio...

A Complete Resolution of the {0,1} Case of Guy's Problem F24

We prove that the only positive integers whose square contains only the digits 0 and 1 are the powers of 10. This settles the {0,1} subcase of Guy's Problem F24. The proof reduces the condition to four exponential Diophantine families. Two quadratic families are excluded by an el...

A Reduction of Guy's Problem D18 to a Genus 5 Fibration over a K3 Surface

Guy's Problem D18 asks whether there exist four distinct positive integers whose squares have all pairwise differences equal to perfect squares. We prove that this problem is equivalent to the existence of a non‑trivial rational point on a family of genus 5 curves fibered over a...