| 5 | For three nonnegative elements of a linearly ordered commutative ring, equality in Schur's cubic inequality holds exactly when all three are equal, or when two are equal and the remaining element is zero.real algebra | 6 | 2/2 |
| 3 | For a real-valued function on a finite set, the sum of the squared pairwise differences equals twice the cardinality times the sum of squares, minus twice the square of the total sum.finite-sum algebra | 12 | 2/2 |
| 2 | For the generalized Lucas sequence defined by U₀ = 0, U₁ = 1, and Uₙ₊₂ = aUₙ₊₁ − bUₙ, the Cassini determinant Uₙ₊₁² − UₙUₙ₊₂ equals bⁿ.algebraic combinatorics | 6 | 2/2 |
| 1 | For every natural number n, there is a prime divisor of n factorial plus one which is strictly larger than n.number theory | 1 | 2/2 |