{"uid":"cap_38UnDdlqsx-UbZbKa6i1Q","slug":"numora-diophantine-equation-solver-72db1600","name":"Numora Diophantine Equation Solver","description":"100 pure math computation endpoints for AI agents. Statistics, financial math, linear algebra, equation solving, calculus, number theory, sequence generation, and unit conversions. Zero external dependencies. x402 micropayments on Base.","url":"https://numormor.netlify.app/api/number/diophantine","method":"POST","headers":{},"bodySchema":{"type":"object","required":["a","b","c"],"properties":{"a":{"type":"integer"},"b":{"type":"integer"},"c":{"type":"integer"}}},"responseSchema":{"type":"object","required":["success","result","computation"],"properties":{"result":{"type":"object","description":"Computation result varies by endpoint"},"success":{"type":"boolean","description":"Always true on success"},"computation":{"type":"string","description":"Human-readable description of what was computed"}}},"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.1","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":{"p10Cents":"10.0000","medianCents":"10.0000","p90Cents":"10.0000","minCents":"10.0000","maxCents":"10.0000","p95Cents":"10.0000","sampleCount":1,"varies":false,"failureChargeRate":1},"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.1/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.1","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.1","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_b6w21lmY_QG91yhnv8Qe4","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.1","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Solves linear Diophantine equations of the form ax + by = c, returning integer solutions if they exist","exampleAgentPrompt":"Can you solve the Diophantine equation where a=17, b=13, and c=1 — I need integer values of x and y that satisfy 17x + 13y = 1?","exampleUseCases":null,"resultDescription":"Returns a JSON object with success=true, a result object containing the particular integer solution (x, y) if one exists (or a flag indicating no solution exists when gcd(a,b) does not divide c), and a human-readable computation string describing what was solved and how.","failureModes":["No solution exists when gcd(a,b) does not divide c — result may indicate unsolvability","Payment failure or 402 response if x402 micropayment is not properly configured","Invalid input types if a, b, or c are not integers — schema validation error","Edge case: a=0 and b=0 with c≠0 is unsolvable; a=0 and b=0 with c=0 is trivially infinite solutions"],"whenToPreferThis":"Use this endpoint when you need exact integer solutions to a linear two-variable equation of the form ax + by = c — a classic number theory problem. Prefer this over general equation solvers when you specifically need integer (not real) solutions, or when applying the extended Euclidean algorithm. Ideal for cryptographic key problems, modular inverse computations, and combinatorial integer constraints.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-14T00:51:32.639Z","isFirstParty":false}