Positive integers $n$ that cannot be written as a sum of $r$ consecutive positive integers, with $r > 1$, are of the form n = $2^l$ for some $l ≥ 0$.
103581
Which positive integers can NOT be written as a sum of consecutive positive integers
42526
The product of $n$ consecutive integers is divisible by $ n!$ (without using the properties of binomial coefficients)
107448
proving that there is no solution for $n$ in positive integers except $n = 1$ for $2^n = nk + 1$
20438
Prove that every positive integer $n$ has a unique expression of the form: $2^{r}m$ where $r\ge 0$ and $m$ is an odd positive integer
150324
Pigeonhole principle: prove that any set of $n+1$ integers from $\{1,2,...,2n\}$ has two consecutive integers differ by one.
46039
Prove that if $x \in R,$ then there exists $n \in Z$ satisfying $x \leq n < x+1$
85817
Show that in any set of $2n$ integers, there is a subset of $n$ integers whose sum is divisible by $n$.
53156
Infinitely many numbers not expressible in the form $a^n+b^n+c^n$
22154
Show that given a set of positive n integers, there exists a non-empty subset whose sum is divisible by n
52542
For which odd positive integer $n$ , is it true that $-1$ is not a positive power of $2$ modulo $n$?
90806
Find all positive integers $n$ such that $n$ is divisible by all the positive integers less than or equal to $\sqrt{n}$
56985
Show that every positive integer has a unique representation in the form $50k+l$...?
22977
How many $6$-integer subsets of $\{1, 2, 3, \ldots, 20\}$ have no consecutive integers?
25338
Sum of $n$ integers from set of size $2n-1$ divides $n$
71650
Proving by strong induction for a sequence of integers, $2^n$ divides term $n$
57746
Prove that, for any set of consecutive integers with an odd number of terms, the sum of the integers is always a multiple of the number of terms.
126161
Interesting property of finite integer sequence with sum 1