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This is a hard one see if you guys can solve it! Try to!

Find the least positive four-digit solution to the following system of congruences.

$\begin{align*} 7x &\equiv 21 \pmod{14} \\ 2x+13 &\equiv 16 \pmod{9} \\ -2x+1 &\equiv x \pmod{25} \\ \end{align*}$

Imcool Dec 4, 2022

Guest · Answer 1 · 2022-12-04T10:14:29

The system reduces to

n = 7 mod 14

n = 6 mod 9

n = 2 mod 25

By the Chinese Remainder Theorem, the smallest four-digit number hat works is 2877.

Imcool · Answer 2 · 2022-12-07T11:43:24

I don't think 2877 is correct..