What is the largest four-digit negative integer congruent to \(1 \pmod{23}\)?
(-x) mod 23 = 1
x =23n + 22, where n =0, 1, 2,3.....etc.
10,000 / 23 =~434
434 - 1 =433
x =23 x 433 + 22 =9,981
(-x) = (-9,981) - the largest negative 4-digit integer.
Because: (-9,981) mod 23 = 1
Seems the LARGEST negative 4 digit number would be
-1011 - 1011 mod 23 = 1
Because -1011 > - 9981
in other words -1011 is larger than -9981
