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2. arithmetic - why is -1 mod 3 = 2? - Mathematics Stack Exchange

   math.stackexchange.com/questions/4013200/why-is-1-mod-3-2

   This is more common in math than in e.g. computer science but it is worth keeping in mind because it simplifies a lot. This is not to say that the choice of 0, 1, 2, ..., b-1 as representatives of a value of a mod b (when a is an integer and "a mod b" is a function output) is not a natural one, which may be what is going on here.

3. What is 1 mod 3? [Solved] - Cuemath

   www.cuemath.com/questions/what-is-1-mod-3

   1 mod 3 equals 1, since 1/3 = 0 with a remainder of 1. To find 1 mod 3 using the modulus method, we first find the highest multiple of the divisor, 3 that is equal to or less than the dividend, 1. Then, we subtract the highest multiple from the dividend to get the answer to 1 mod 3. Multiples of 3 are 0, 3, 6, 9, etc. and the highest multiple ...

4. proof that there are infinitely many primes congruent to $1$ mod...

   math.stackexchange.com/questions/2256680

   There seems to be a fundamental difference between $2\pmod3$ and $1\pmod3$ in this way (similarly, between $3\pmod4$ and $1\pmod4$). $\endgroup$ – Greg Martin Commented Apr 28, 2017 at 20:07

5. Congruence $n*2^n + 1 \\mod 3$ - Mathematics Stack Exchange

   math.stackexchange.com/questions/3323493/congruence-n2n-1-mod-3

   Let n be even, then n2n + 1 ≡ n(1) + 1 (mod3) ≡ n + 1 (mod 3) We want this to be 0 mod3, so n ≡ 2 (mod3). We have the following conditions on n, n ≡ 0 (mod 2) and n ≡ 2 (mod 3). This can be consolidated as n ≡ 2 (mod 6). Likewise you can deal with the other case. This was very helpful, thanks.

6. For any integer $n$, $n^2$ is congruent to $0$ or $1$ modulo $3$

   math.stackexchange.com/.../for-any-integer-n-n2-is-congruent-to-0-or-1-modulo-3

   We can check that $0^2\cong0\pmod 3$, $1^2\cong1\pmod 3$, and $2^2\cong4\cong1 \pmod3$. There are only three cases to check. There are only three cases to check. Share

7. Proving $10^n \\equiv 1 \\pmod 3$ for all $n\\geq 1$ by induction

   math.stackexchange.com/questions/1238361/proving-10n-equiv-1-pmod-3-for-all-n...

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8. Show that for every integer $n$, $n^3 - n$ is divisible by 3...

   math.stackexchange.com/questions/2292586

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9. Primes congruent to 1 (mod 3) - Mathematics Stack Exchange

   math.stackexchange.com/questions/2208009/primes-congruent-to-1-mod-3

   1. Assume that x, y are integers, and f(x, y) = x4 − 2x3y + x2y2 − y4 is a prime number greater than 3. Prove that f(x, y) ≡ 1 (mod3). For example, f(34, 21) = 883 is a prime and 883 ≡ 1 (mod 3). [ Hint: x4 − 2x3y + x2y2 − y4 = (x2 − xy + y2)(x2 − xy − y2). Ive tried many of the modular arithmetic tricks I know but I can't get ...

10. elementary number theory - Legendre symbol $(-3/p)$ where $p = 1...

    math.stackexchange.com/questions/1501799/legendre-symbol-3-p-where-p-1-mod-3

    Suppose $p = 1 \bmod 3$, prove the following statements: prove that $x^2 + x + 1 = 0 \mod p$ has a solution ...

11. $p = x^2 + xy + y^2$ if and only if $p \\equiv 1 \\text{ mod }3$?

    math.stackexchange.com/questions/1722377

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