Show that for any integer not divisible by 2 or 5, there is a multiple of it which is a string of 1s.
66623
Primes dividing $11, 111, 1111, ...$
51638
pigeonhole principle divisibility proof
28579
Creating a sequence that does not have an increasing or a decreasing sequence of length 3 from a set with 5 elements
76434
What is the measure of the set of numbers in $[0,1]$ whose decimal expansions do not contain $5$?
18108
Show if $(a,p)=1$ there is a unique inverse of $a$ modulo $p$
100336
Find an integer having the remainders $2,3,4,5$ when divided by $3,4,5,6$, respectively.
127033
Prove reversal of a string by induction
35648
How many permutations of the set n={1,2,3,3,3,4,4,5} are possible without any consecutive identical elements?
150324
Pigeonhole principle: prove that any set of $n+1$ integers from $\{1,2,...,2n\}$ has two consecutive integers differ by one.
8364
To show that Fermat number $F_{5}$ is divisible by $641$.
42744
Prove a number is even using the Pigeonhole Principle
20174
Discrete mathematics bit strings
31708
Divisibility criteria for $7,11,13,17,19$
64052
Among any three consecutive positive integers one is a multiple of 3
33866
Show that $n$ does not divide $2^n - 1$ where $n$ is an integer greater than $1$?
48908
Choose 100 numbers from 1~200 (one less than 16) - prove one is divisible by another!
99912
Any digit written $6k$ times forms a number divisible by $13$