{"uid":"cap_Wx4ZnfNdzL6ClVxADfs9w","slug":"numora-diophantine-equation-solver-da7a020b","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://numormo.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_LWAWy7F1EsSKMViQVBi0d","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 a linear Diophantine equation of the form ax + by = c, returning integer solutions if they exist","exampleAgentPrompt":"Can you find integer solutions to the equation 12x + 8y = 4? I need values of x and y that are whole numbers.","exampleUseCases":[{"title":"Checking coin combination feasibility","prompt":"I need to know if it's possible to make exactly 37 cents using only 5-cent and 8-cent tokens — can you find integer solutions to 5x + 8y = 37?"},{"title":"Modular arithmetic problem solving","prompt":"I'm working on a number theory homework problem: find integer solutions for x and y where 14x + 21y = 7."},{"title":"Resource allocation with integer constraints","prompt":"I need to figure out how many packages of 6 and packages of 9 I can combine to get exactly 24 items total — solve 6x + 9y = 24 for non-negative integers."}],"resultDescription":"Returns a JSON object with a 'success' boolean, a 'result' object containing the particular integer solution (x, y), the GCD of a and b, the general solution parameterization, and whether solutions exist, plus a human-readable 'computation' string explaining what was computed.","failureModes":["No integer solution exists when GCD(a,b) does not divide c — returns solvability false or error","Non-integer inputs cause validation failure","Missing required fields a, b, or c result in a 400-level error","Both a and b equal zero with non-zero c is undefined/unsolvable","Payment failure or insufficient funds returns 402"],"whenToPreferThis":"Use this endpoint when you need exact integer solutions to a two-variable linear equation (ax + by = c) without any floating-point approximation. Prefer it over general numeric solvers when integer-only solutions are required, such as in number theory, combinatorics, or discrete resource allocation problems. It is purpose-built for Diophantine equations and provides the general solution family, not just one answer.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-14T18:52:50.658Z","isFirstParty":false}