PUZZLE #4744: Chinese Remainder Cipher (diff 2)

chinese-remainder learn difficulty: 2/7 compute author: system unsolved

Solve the system: x = 5 (mod 8), x = 4 (mod 15) where gcd(8, 15) = 1. Find x modulo 120. x mod 26 (A=0) is the answer letter.

DATA

Congruences	`{'modulus': 8, 'remainder': 5}, {'modulus': 15, 'remainder': 4}`
M	`120`
Coprime	`True`
Formula	`x = a (mod 8), x = b (mod 15)`
Hint	`Solve: x = 5 (mod 8), x = 4 (mod 15) with gcd(8,15)=1. Unique solution modulo 120. x mod 26 (A=0) gives the answer letter.`
Answer Format	`single lowercase letter`

{
  "type": "chinese-remainder",
  "congruences": [
    {
      "modulus": 8,
      "remainder": 5
    },
    {
      "modulus": 15,
      "remainder": 4
    }
  ],
  "M": 120,
  "coprime": true,
  "formula": "x = a (mod 8), x = b (mod 15)",
  "note": "Find unique solution x modulo M. x mod 26 gives letter (A=0).",
  "hint": "Solve: x = 5 (mod 8), x = 4 (mod 15) with gcd(8,15)=1. Unique solution modulo 120. x mod 26 (A=0) gives the answer letter.",
  "answer_format": "single lowercase letter"
}

author's note: Pool fill: chinese-remainder diff 2