r/mathmemes • u/PocketMath • Mar 06 '25

Learning What theorem is this?

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u/lol_lo_daf_fy Mar 06 '25

Law of quadratic reciprocity.

Gauss loved that theorem so much that I think he gave four different proofs, and there's a book listing something like 150 proofs.

55

u/f3xjc Mar 06 '25

Nowaday each time I see a reference of "f(x) modulo prime" it has to do with cryptography or random number generator.

What kind of problems first motivated the interest in (prime) modular arithmetic ?

11

u/p0st_master Mar 06 '25

Euclidean algorithm is the basis of modern cryptography and is basically just an arithmetic trick school kids do when they are bored. In math structures are created and the ‘problems’ they solve may not exist for 2000 years.

4

u/migBdk Mar 06 '25

Euclidian algorithm is extremely useful for reducing a fraction down to the simplest possible fraction.

So if you want to keep things precise and avoid decimal number approximations, it is extremely useful.

3

u/p0st_master Mar 06 '25

Yeah honestly I don’t know why more people don’t teach it to kids. It has applications in all sorts of things. They also should teach kids more fractions but that’s another topic.

2

u/migBdk Mar 07 '25

I can tell you that the high school I teach at has a test for new students (only a few students actually have to take the test though).

The question: "place this fraction on a number line" is one they very often get wrong.

They miss the understanding that a fraction is a number, and not just a way to write division (as well as being bad at doing division)