Answer Key — Diophantine equations and cryptography
Number theory
Do not share with students before practice tests.
Worksheets — Sets 1–10
| Set | Guidance | | --- | --- | | Set 1 | Diophantine equations and cryptography — verify written work and accept reasonable drawings. | | Set 2 | Diophantine equations and cryptography — verify written work and accept reasonable drawings. | | Set 3 | Diophantine equations and cryptography — verify written work and accept reasonable drawings. | | Set 4 | Diophantine equations and cryptography — verify written work and accept reasonable drawings. | | Set 5 | Diophantine equations and cryptography — verify written work and accept reasonable drawings. | | Set 6 | Diophantine equations and cryptography — verify written work and accept reasonable drawings. | | Set 7 | Diophantine equations and cryptography — verify written work and accept reasonable drawings. | | Set 8 | Diophantine equations and cryptography — verify written work and accept reasonable drawings. | | Set 9 | Diophantine equations and cryptography — verify written work and accept reasonable drawings. | | Set 10 | Diophantine equations and cryptography — verify written work and accept reasonable drawings. |
Worksheets — Sets 11–20
| Set | Guidance | | --- | --- | | Set 11 | Diophantine equations and cryptography — verify written work and accept reasonable drawings. | | Set 12 | Diophantine equations and cryptography — verify written work and accept reasonable drawings. | | Set 13 | Diophantine equations and cryptography — verify written work and accept reasonable drawings. | | Set 14 | Diophantine equations and cryptography — verify written work and accept reasonable drawings. | | Set 15 | Diophantine equations and cryptography — verify written work and accept reasonable drawings. | | Set 16 | Diophantine equations and cryptography — verify written work and accept reasonable drawings. | | Set 17 | Diophantine equations and cryptography — verify written work and accept reasonable drawings. | | Set 18 | Diophantine equations and cryptography — verify written work and accept reasonable drawings. | | Set 19 | Diophantine equations and cryptography — verify written work and accept reasonable drawings. | | Set 20 | Diophantine equations and cryptography — verify written work and accept reasonable drawings. |
Review tiers 1–10
- Checklists are parent-judged.
- Written items: verify against practice set patterns.
- Standard text: Pythagorean triples and primitive solutions Sums of two squares (introduction) Continued fractions (optional topic) RSA and public-key cryptography from number-theoretic primitives Introduction to algebraic number theory: Gaussian integers (optional)
Practice test scoring
| Tier | Pass guidance | | --- | --- | | 1–3 | Most oral tasks smooth; majority of written correct | | 4–6 | 7/10+ total with clear understanding | | 7–8 | 9/12+ with explanations | | 9–10 | Near-perfect; ready to move on |
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