Prove if $n$ is an odd integer, then $3n$ is odd.
114796
Direct proof that the product of odd integers is odd
2900
How many $3$-subsets of $\{1,2,\ldots,10\}$ contain at least one even and one odd integer?
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
95889
Prove that $\gcd(n! + 1, 3n! + 1) = 1$, $\forall n \in \mathbb{N}$, $n \geq 2$.
69575
If $ad$ and $bc$ are odd and even, respectively, then prove that $ax^3+bx^2+cx+d$ has an irrational root.
83307
If $n\mid a^2-1$, $n$ an odd integer, show $n = \gcd(a-1, n)\gcd(a+1, n)$
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.
60738
If 4n+1 and 3n+1 are both perfect sqares, then 56|n. How can I prove this?
66358
Prove by mathematical induction that $2n ≤ 2^n$, for all integer $n≥1$?
96097
Let $k$ be an odd positive integer. Prove that $(1+2+3...+n)|(1^k+2^k+3^k+...+n^k)$ for all positive integers $n$.
27063
Prove that if n is an odd positive integer , then $n^2\equiv1\mod8$
54359
Odd Primes Problem Proof
104010
The number of partitions of $n$ into distinct parts equals the number of partitions of $n$ into odd parts
144447
Show that $504 \mid (n^9 − n^3 )$ for any integer $n$
21612
How to prove this form of $n$?
77816
Proof problem: Show that $n^2-1$ is divisible by $8$, if $n$ is an odd positive integer.
130488
Prove by induction that $3\mid n^3 - n$