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  1. Does ⋮ mean "is divisible by" in mathematical notation?

    Nov 14, 2020 · The only way in normal notation to write it is $5\mid 5 (2+3m).$ I don’t know of a standard symbol for “a is divisible by b.”

  2. Prove that $a^ {2n} -b^ {2n}$ is divisible by $a+b$ [duplicate]

    Jul 1, 2019 · 2 This question already has answers here: Why is $a^n - b^n$ divisible by $a-b$? (8 answers)

  3. Is $b\mid a$ standard notation for $b$ divides $a$? [duplicate]

    This is the standard way, in the specific meaning of compliance to international standards: ISO 80000-2, clause 2.7-17. Note that the vertical bar character used there is normatively identified …

  4. Divisibility by 7 - Mathematics Stack Exchange

    The best way to test if a number is divisible by any other number is by deducting the number n times and check whether the remainder is divisible by n. for example 861-7n/7.

  5. How to prove the divisibility rule for $3\, $ [casting out threes]

    Mar 26, 2013 · iff xyz= (100x)+ (10y)+z=x+y+z=0 (mod3) Therefore x+y+z=0 (mod 3), meaning that the sum of the digits is divisible by 3. This is an if and only if statement. You can generalize …

  6. elementary number theory - What is meant by "evenly divisible ...

    "What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?" Is it different from divisible?

  7. Proof of the divisibility rule of 11. - Mathematics Stack Exchange

    Sep 27, 2021 · We know, A number is divisible by $11$ if the difference of the sum of the digits in the odd places and the sum of the digits in the even places is divisible by $11$. For example, …

  8. Divisibility of 9 trick: why does it work? [duplicate]

    Jan 19, 2020 · I've been wondering ever since I learned about the divisibility of nine trick. Add up the sum of the digits. If the sum is a multiple of nine, the entire number is divisible by nine. If …

  9. Prove by induction $6\cdot 7^n -2\cdot 3^n$ is divisible by $4$ for …

    Feb 1, 2014 · Write out the formula for the case $n + 1$ and then subtract the formula for the case $n$. Is the result divisible by $4$? If so does that help you?

  10. Prove by induction $5^{2n} − 1$ is divisible by $8$ for all $n ∈ N$.

    May 8, 2023 · I now know the formula for proof by induction, but I still don't understand what it intrinsically means or how it guarantees $5^ {2n} − 1$ is divisible by $8$ for all $n ∈ N$.