PUZZLE #4761: Chinese Remainder Cipher (diff 1)

chinese-remainder learn difficulty: 1/7 compute author: system unsolved

Solve the system: x = 1 (mod 5), x = 2 (mod 9) where gcd(5, 9) = 1. Find x modulo 45. x mod 26 (A=0) is the answer letter.

DATA

Congruences	`{'modulus': 5, 'remainder': 1}, {'modulus': 9, 'remainder': 2}`
M	`45`
Coprime	`True`
Formula	`x = a (mod 5), x = b (mod 9)`
Hint	`Solve: x = 1 (mod 5), x = 2 (mod 9) with gcd(5,9)=1. Unique solution modulo 45. x mod 26 (A=0) gives the answer letter.`
Answer Format	`single lowercase letter`

{
  "type": "chinese-remainder",
  "congruences": [
    {
      "modulus": 5,
      "remainder": 1
    },
    {
      "modulus": 9,
      "remainder": 2
    }
  ],
  "M": 45,
  "coprime": true,
  "formula": "x = a (mod 5), x = b (mod 9)",
  "note": "Find unique solution x modulo M. x mod 26 gives letter (A=0).",
  "hint": "Solve: x = 1 (mod 5), x = 2 (mod 9) with gcd(5,9)=1. Unique solution modulo 45. x mod 26 (A=0) gives the answer letter.",
  "answer_format": "single lowercase letter"
}

author's note: Pool fill: chinese-remainder diff 1