How to prove that there are infinitely many integers n for which each of n, n+1, . . . ,n+ 1000 is composite.
65757
Prove that $n! + k$ is a composite number
149216
Give a combinatorial proof to show the following for all integers $n \geq 2$.
89175
Proof of $(a+b)^{n+1}$
98468
Are there infinitely many primes of the form $n!+1$?
142956
Prove that for any positive integer n there is a sequence of n consecutive composite numbers.
138409
Proof of infinitely many primes, clarification
46803
Proof that there are infinitely many primes congruent to 3 modulo 4
38748
There are infinitely many prime numbers $p$ for which $p + 2$ and $p + 4$ are also prime numbers
82482
Proving an infinite number of primes of the form 6n+1
144592
how to prove the existence and uniqueness of the prime factorization of any natural number.
33177
All numbers of form $10^{k} + 1$ are composite for $k{\gt}2$ proof
91285
Prove $a+b+c+d $ is composite
56574
For any integer $a,b$ let $N_{a,b}$ denote the number of positive integer $x<1000$ satisfying $x= a( mod\;27)$ and $x=b(mod\;37)$. Then
24954
Prove that there are infinitely many integers of the form $111\ldots111$ that are multiple of $n$.
107381
Understanding the proof of infinitely many primes $\equiv 3\pmod{\!4}$
44745
How many positive integers less than 1000 have distinct digits and are even?
56985
Show that every positive integer has a unique representation in the form $50k+l$...?