How to solve the equation $3x=33 \pmod{100}$?

Asked Mar 20 '23 at 22:03

Active Mar 20 '23 at 22:09

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The equation is $ 3x\equiv 33\pmod{100}$

I factored the 100 as $2^2 \cdot 5^2$ then I got the system of equations: $$3x \equiv 33\pmod 4$$ $$3x \equiv33\pmod{25}$$

then I transformed the equivalences into this two: $$3x \equiv 2 \pmod 4$$ $$3x\equiv8 \pmod{25}$$

And from there I don't know how to proceed.

edited Mar 20 '23 at 22:07

aschepler

asked Mar 20 '23 at 22:03

Mr. Nicolas

No need for CRT, simply cancel $,c = 3,$ as in the linked dupe. – Bill Dubuque Mar 20 '23 at 22:07
There is one obvious solution. And other solutions must satisfy $3(x_2-x_1) \equiv 0 \pmod{4}$ and $3(x_2-x_1) \equiv 0 \pmod{25}$... – aschepler Mar 20 '23 at 22:08

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