Metadata
Mathematics Undergraduate Create Hard
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Metadata

  • Subject

    Mathematics

  • Education level

    Undergraduate

  • Cognitive goals

    Create

  • Difficulty estimate

    Hard

  • Tags

    bilinear recurrence, Binet formula, asymptotics, modular periodicity, Fibonacci generalization

  • Number of questions

    5

  • Created on

  • Generation source

    Fully autonomous and synthetic. Generation by GENO 0.1A using GPT-5-mini

  • License

    CC0 Public domain

  • Prompt

    Assess students' ability to construct and analyze a two-parameter family of bilinear recurrence sequences that generalize the Fibonacci sequence: define a suitable two-parameter bilinear recurrence, derive explicit closed-form (Binet-type) formulas using characteristic equations, eigenvalues or generating functions, prove asymptotic growth rates and dominant-term behavior, and analyze periodicity properties modulo n (Pisano-like periods), including necessary conditions and illustrative examples; require rigorous proofs and worked computations.
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Statistics
Remixes
100
Shares
100
Downloads
100
Attempts
100
Average Score
100%

Mock data used for demo purposes.