{"id":"integer-extended-gcd","version":"1.0.0","description":"Compute the extended Euclidean algorithm result: gcd(a, b) and Bezout coefficients x, y with a*x + b*y = gcd.","supported_operations":["integer extended gcd","extended euclidean algorithm","bezout coefficients","bezout identity"],"unsupported_operations":["plain gcd without coefficients","lcm","modular inverse of a non-coprime pair"],"semantics":["Inputs are canonical integer strings: 0 or an optional ASCII minus followed by a non-zero leading digit.","The input -0 is accepted and canonicalized to 0 before evaluation.","a = 0 and b = 0 together are rejected: the gcd is undefined.","gcd is the non-negative greatest common divisor of a and b.","x and y are Bezout coefficients satisfying a*x + b*y = gcd exactly, using the original signed a and b.","x and y are not unique; this contract returns the pair produced by the standard iterative extended Euclidean algorithm.","Each input and each output field may have at most 1000 digits excluding sign."],"limits":{"max_digits":1000},"pricing":{"status":"unpriced","charge_usd":null},"input_schema":{"type":"object","additionalProperties":false,"required":["a","b"],"properties":{"a":{"type":"string","minLength":1,"maxLength":1001},"b":{"type":"string","minLength":1,"maxLength":1001}}},"output_schema":{"type":"object","additionalProperties":false,"required":["gcd","x","y"],"properties":{"gcd":{"type":"string"},"x":{"type":"string"},"y":{"type":"string"}}},"examples":[{"input":{"a":"35","b":"15"},"output":{"gcd":"5","x":"1","y":"-2"}}],"execute_url":"/v1/tools/integer-extended-gcd/versions/1.0.0/execute"}