Math Major Examples -- Number Theory #10

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[DendrocnideMoroides]

please add this video to the number theory playlist

[user]

The last problem does not work if p=2 as the sum would be just 1 and clearly 1 is not divisible by 2.
Furthermore, since we can always multiply the same thing to the numerator and the denominator of a fraction(except when it is 0), so we could technically cheat by saying the fraction a/b is (ap)/(bp) which "proves" that the numerator (ap) is divisible by p. So the statement should have been more carefully stated.

[SanketAlekar]

You have an error in example 4. 23, 24, ...31 is 1, 2, 3...9 mod 11. (you have it as up to 8). So the correct answer is 1 mod 11.

[corbinsmith]

The title card is says (p-1) is congruent to -1 mod p, forgot the factorial

[krisbrandenberger]

In the last example, the denominators of the sums of the pairs of terms in each of the sets of parentheses must add to give p.

[schweinmachtbree]

typo in the last solution, it should be (1/2 + 1/(p-2)) not (2 + 1/(p-2)). (and as someone has already pointed out, the solution only works for odd primes because the problem statement is wrong; the statement is only true for odd primes)

[stefanschroder]

You are too fast and that's reason for sloppy mistakes

[leif]

How or why would.anyone derive or discover this theorem? Indont see how or why anyone would
. Can you share a video on thst..