Khaled Mohammed Ahmed Saad Albakali

A Unique Characterization of the Number 17 via Digit-Sum Square Conditions

We prove that the number 17 is the unique integer n ≥ 10 satisfying the simultaneous conditions: n - s(n) = a², n + s(n) = b², where s(n) denotes the sum of the decimal digits of n and a, b are non-negative integers. We further show that adding the condition √(n-1) ∈ ℤ preserves...