#Help in a Modular Arithmetic equation

1 messages · Page 1 of 1 (latest)

analog sorrel
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How do I solve for x in this modular arithmetic equation (a is equal to 11 in this equation) (See first pic)?
I believe that I have to use the Extended Euclidean Algorithm. According to my lecture notes, the easiest way to do this is with the FISH algorithm (Here is an example of the algorithm in action in the second pic):
However, I don’t know how to rearrange the equation in order to perform this algorithm.
I would really appreciate any assistance from you guys!

20231009_112824.jpg 20231009_112951.jpg
rocky nexusBOT
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queen verge
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,w 3^10

vague owlBOT
queen verge
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wait what

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what is the modulo equal to

analog sorrel
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It's mod 9743 according to he first picture. Did I misunderstood the question?

queen verge
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oh that makes a lot more sense

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I’ve only seen mods notated a triple equals (mod b) lmao

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131221 looks like it simplifies very nicely if you just take its mod

analog sorrel
queen verge
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yea

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so once you simplify the 131221

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you can then isolate your 292x

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actually its 297x

analog sorrel
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I think I might have made a mistake in the 4th line. I was going under the assumption of the Distributive property from basic Arithmetic, but that might me the wrong approach

20231009_143709.jpg
queen verge
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thats good yea

analog sorrel
queen verge
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does x have to be an integer or no

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wait also are we in mod 9743 or mod 59049

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when you take the mod of something the answer is usually lower than whatever the mod is...?

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ive never formally learned mods i just learned them for math contests so sorry if im just completely wrong

analog sorrel
queen verge
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oh

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do you know which number is the mod number and which one is the result

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is it 3^10?

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find it very weird the result is much higher than the mod number

analog sorrel
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According to the picture, 3^10 seems to be at the right side of the equation, so I guess it's the result?

queen verge
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imma wait for a more experienced helper i guess

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it does seem like 3^10 is the result but its WAYYY over 9743 so its very strange

analog sorrel