Show that if N is relatively prime to 10, then there exists a multiple that consists only of 1s.
42289
prove that there are infinitely many numbers of the form $x = 111....1$ such that $31\mid x$
2884
$m,n>1$ are relatively prime integers , then are there at-least four idempotent (w.r.t. multiplication) elements in $\mathbb Z_{mn}$ ?
75685
Prove that there is prime number and natural so $n\times q$ digits are $1$.
73515
Primes Number Theory
100613
Prove that if an average of a thousand numbers is less than 7, then at least one of the numbers being averaged is less than 7
99890
Primes with digits only 1
24954
Prove that there are infinitely many integers of the form $111\ldots111$ that are multiple of $n$.
47471
The square of n+1-th prime is less than the product of the first n primes.
131385
How to provide a counterexample for if $n$ is prime, then $2^n -1$ is prime
27069
sum of all positive integers less than $n$ and relatively prime to $n$
158106
Prove that 1 less than the number of equivalence classes divides $p-1$ where $p$ is prime
43567
Some hints for "If a prime $p = n^2+5$, then $p\equiv 1\mod 10$ or $p\equiv 9\mod 10$"
86902
Consider the smallest number in each of the $n\choose r$ subsets (of size $r$) of $S=\{1,2,\ldots,n\}$...
9319
If $n\ne 4$ is composite, then $n$ divides $(n-1)!$.
139350
Given two coprime integers, find multiples of them that differ by 1
121614
Count how many number are there from $1$ to $N$ who have all $10$ digits in it at least once.
134963
Proving a non-prime (composite) number $> 1$ has a divisor $d \leq\sqrt q$