Prove some member of the sequence $7, 77, 777, 7777, \\dots$ is . . . As $10^x$ is not divisible by 2019 then $\underbrace{777\cdots777}_{(y-x) \,\text{digits}}$, which is the $(y-x)$-th element of the given sequence, must be divisible by 2019 It is contradictory to my assumption in the beginning The proof by contradiction is complete Some elements of the given sequence are divisible by 2019
Does ⋮ mean is divisible by in mathematical notation? $\begingroup$ 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 ” $\endgroup$ – Thomas Andrews Commented Nov 14, 2020 at 3:13
elementary number theory - What is meant by evenly divisible . . . It sort of makes sense to qualify divisible, when one means that the quotient is an integer After all, $5 20=0 25$ But the fact is that in mathematics beyond school mathematics, "evenly divisible" is uncommon $\endgroup$
number theory - Divisibility by 7. - Mathematics Stack Exchange I know that to determine if a number is divisible by $7$, take the last digit off the number, double it and subtract the doubled number from the remaining number If the result is evenly divisible by $7$ (e g $14, 7, 0, -7$, etc ), then the number is divisible by seven
elementary number theory - Divisibility Tests for Palindromes . . . A non-zero palindrome is divisible by $5$ if and only if it starts with a $5$ Both of these examples are found by applying some well known divisibility rules The example of what I'm looking for is the case of the divisibility rule for $11$, which lets on simply check the alternating sum of the digits
Is $0$ divisible by $0$? - Mathematics Stack Exchange But, that is a moot point since the question being asked is very explicitly "is $0$ divisible by $0$" which does not need any knowledge about nor need to make any reference to the expression $0 0$ and what it may or may not evaluate to or whether it is considered a valid expression $\endgroup$ –