Prove some member of the sequence $7, 77, 777, 7777, \dots$ is ...
Oct 5, 2020 · Prove that some member of the sequence $7, 77, 777, 7777, \dots$ is divisible by $2019$. So far I have figured that as $2019$ is divisible by $3$, then if one of the terms of the sequence $$ …
Does ⋮ mean "is divisible by" in mathematical notation?
Nov 14, 2020 · Does ⋮ mean "is divisible by" in mathematical notation? Ask Question Asked 5 years, 3 months ago Modified 2 years, 4 months ago
Is $b\\mid a$ standard notation for $b$ divides $a$?
This is the standard way, in the specific meaning of compliance to international standards: ISO 80000-2, clause 2.7-17. Note that the vertical bar character used there is normatively identified as U+2223 …
elementary number theory - Why is $a^n - b^n$ divisible by $a-b ...
I also see that $6^n$ $- 5n + 4$ is divisible by $5$ which is $6-5+4$ and $7^n$$+3n + 8$ is divisible by $9$ which is $7+3+8=18=9\cdot2$. Are they just a coincidence or is there a theory behind?
combinatorics - How many 7-digit numbers with distinct digits can be ...
Nov 29, 2023 · How many 7-digit numbers with distinct digits can be made that are divisible by 3? First of all, I counted all the ways to insert 7 of 10 digits in a number making the number divisible by 3.
abstract algebra - Injective modules and divisible modules ...
Dec 28, 2024 · Injective modules and divisible modules Ask Question Asked 1 year, 1 month ago Modified 1 year, 1 month ago
Prove that a number is divisible by 3 iff the sum of its digits is ...
Sep 30, 2015 · Every term on the right other than the sum of the digits is divisible by $3$. So the remainder when dividing the original number by $3$ and the sum of the digits by $3$ must be the same.
Why are all non-prime numbers divisible by a prime number?
Why a non-prime is always divisible by a prime? When a number P is divisible by n1 then n1 is a factor of P. For example P = n1 x n2 x n3. So P is divisible by either n1, n2, n3 (the quotient is a positive …
The sum of the cubes of three consecutive integers is divisible by $9$
Oct 25, 2017 · The sum of the cubes of three consecutive integers is divisible by $9$ [duplicate] Ask Question Asked 8 years, 4 months ago Modified 6 years, 3 months ago
Prove by mathematical induction that $(3n+1)7^n -1$ is divisible by $9 ...
Nov 30, 2019 · Prove by mathematical induction that $ (3n+1)7^n -1$ is divisible by $9$ for integral $n>0$ [duplicate] Ask Question Asked 6 years, 2 months ago Modified 2 months ago