{"uid":"cap_XZcufIkO5Qne46uRK64ef","slug":"numora-diophantine-equation-solver-31f8bd03","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://numomo.vercel.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":"registry","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"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_zqn_T7qJgyy2clfSgXQT0","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.1","costPer":"request","priority":0,"asset":null,"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 3x + 7y = 1 and find integer values of x and y that satisfy it?","exampleUseCases":[{"title":"Cryptography key relationship check","prompt":"I need to find integer solutions to the equation 17x + 5y = 1 — can you solve this Diophantine equation and give me the general solution?"},{"title":"Resource allocation integer constraint","prompt":"I have the equation 6x + 9y = 12 and I need to know if there are integer solutions and what they are — can you solve this for me?"},{"title":"Verify Bezout identity coefficients","prompt":"Can you solve the Diophantine equation 35x + 15y = 5 and tell me if integer solutions exist, and if so what x and y values work?"}],"resultDescription":"Returns a success flag, a human-readable description of the computation, and a result object containing whether integer solutions exist, a particular solution (x0, y0) if solvable, the GCD of a and b, and the general solution parametric form (e.g. x = x0 + (b/gcd)t, y = y0 - (a/gcd)t for any integer t).","failureModes":["Both a and b are zero (undefined equation, no unique solution)","c is not divisible by gcd(a, b) meaning no integer solution exists — endpoint returns success:true but indicates unsolvable","Non-integer inputs rejected with 400 error","Missing required fields a, b, or c return validation error","Payment not included or insufficient triggers x402 payment required response"],"whenToPreferThis":"Choose this endpoint when you need to solve a two-variable linear equation strictly over the integers (Diophantine form ax + by = c), particularly in number theory, cryptography (Bezout coefficients), modular arithmetic, or combinatorial resource allocation problems. Prefer over general equation solvers when integer constraints are mandatory and you need the complete parametric family of solutions.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-15T12:33:30.149Z","isFirstParty":false}