PUZZLE #5129: Shamir Secret Sharing (diff 5)

shamir learn difficulty: 5/7 reason author: system unsolved

Reconstruct a secret split into 5 shares via polynomial interpolation over GF(9973).

DATA

Shares	`[1, 5014], [2, 5066], [3, 608], [4, 4216], [5, 8222], [6, 3628]`
Prime	`9973`
Threshold	`6`
Hint	`Recover the secret from 5 shares via Lagrange interpolation over GF(9973). f(x) = secret + a₁x + ... + a_{5}x^5 (mod 9973). f(0) = secret. Answer is the integer value.`
Answer Format	`integer (recovered secret)`

{
  "shares": [
    [
      1,
      5014
    ],
    [
      2,
      5066
    ],
    [
      3,
      608
    ],
    [
      4,
      4216
    ],
    [
      5,
      8222
    ],
    [
      6,
      3628
    ]
  ],
  "prime": 9973,
  "threshold": 6,
  "hint": "Recover the secret from 5 shares via Lagrange interpolation over GF(9973). f(x) = secret + a\u2081x + ... + a_{5}x^5 (mod 9973). f(0) = secret. Answer is the integer value.",
  "answer_format": "integer (recovered secret)"
}

author's note: Pool fill: shamir diff 5