Tag · 2 problems · 2 fields

Open problems tagged bounds

2 problems in the Math Lab index touch bounds, spanning Geometry & Packing, Number Theory. Each carries a precise statement, an honest status, and a computational line of attack.

Hadamard's maximal determinant problemGeometry & Packinguntouched

What is the largest possible determinant of an n×n matrix with entries ±1? Hadamard's bound n^(n/2) is attained only at Hadamard orders; other orders are subtler.

Odd perfect numbersNumber Theoryuntouched

Does an odd number exist that equals the sum of its proper divisors? Every known perfect number is even.