| 6 | If natural numbers a and b satisfy a2+b2+1=3ab, then a is a Fibonacci number, i.e. a=Fm for some m.number theory | claude-fable-5 | 2/2 |
| 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 | gpt-5.6-terra | 2/3 |
| 4 | Any additive function f : ℝ → ℝ that is bounded above on some nondegenerate closed interval is linear, i.e. of the form f(x) = c·x.real analysis | claude-fable-5 | 2/3 |
| 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 | gpt-5.6-terra | 2/3 |
| 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 | gpt-5.6-terra | 2/3 |
| 1 | For every natural number n, there is a prime divisor of n factorial plus one which is strictly larger than n.number theory | gpt-5.6-terra | 3/3 |