#a way to calculate remainder of big numbers

70 messages · Page 1 of 1 (latest)

civic trellis
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I'm currently self studying modular arithmeric, is there a way to calculate the remainder of big numbers? For example 2,000^2,000 mod 7, I tried something like factoring 2,000 into smaller numbers but idk if I'm going the right direction or not

plucky glenBOT
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echo stream
civic trellis
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That's what i remember it as the last time I looked it up

echo stream
civic trellis
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I think so but I couldn't remember it well since that was like a month ago

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That time I was just looking up random stuff that I got interested in

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I'll watch an explanation again, then see if I can solve it on my own, thanks

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@echo stream question

echo stream
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Yes?

civic trellis
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Am I suppose to apply the crt to solve it?

echo stream
civic trellis
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For big numbers

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Or do I watch it just to understand some stuff needed for solving it

echo stream
civic trellis
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I see

echo stream
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I am a bit rusty in crt as well, so I am also learning lol.

civic trellis
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Oh thanks!

cold nacelle
# civic trellis Oh thanks!

It doesn't actually have anything to do with the Chinese Remainder Theorem. You need to learn Euler's Theorem, or its more restricted form Fermat's Little Theorem.

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The Chinese Remainder Theorem is about systems of congruences, but we don't have a system here.

civic trellis
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Oh

echo stream
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Oh wait nvm I got it.

civic trellis
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Ah a^p = a(mod p)

echo stream
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Sorry for the mishap.

civic trellis
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What do you mean

cold nacelle
civic trellis
cold nacelle
civic trellis
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Huh?

cold nacelle
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What are the sides here?

civic trellis
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When I tried solving this stuff I just compare the left side with something else then exponent it like 5 congruence to 1 (mod 4)
So 5^3 congruence to 1^3 (mod4)

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Does it not work here?

cold nacelle
civic trellis
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Wait I'm confused

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5^n is the left side?

cold nacelle
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What n? Where did n come from?

civic trellis
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I just tried giving an example

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One sec

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Oh nevermind it's too big

cold nacelle
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...too big to... have n or...???

civic trellis
cold nacelle
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...why would it be congruent to that?

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Also that still doesn't explain to me where n came from.

civic trellis
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Isn't 2000 congruent to 5?

cold nacelle
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And how can something to the power of n be "too big"?

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"Too big" for what?

civic trellis
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Nevermind

cold nacelle
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Okay, look.

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We have one thing.

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2000^2000 mod 7.

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It's not an equation.

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it's not a congruence.

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There's no "left side" or "right side".

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It's just an expression.

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We're evaluating the expression.

civic trellis
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Oh

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Is it ok to do something to the expression?

cold nacelle
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Depends on what it is.

civic trellis
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I did something like this

20240410_134754.jpg
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I think all I have to do is just use an exponent that makes it so the other side is 1,-1 but I'm not sure if it'll always work for big numbers

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Thank you btw @cold nacelle @echo stream

odd pastureBOT
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@civic trellis has given 1 rep to @echo stream @cold nacelle

cold nacelle
echo stream
civic trellis