how to proof that $1,9999.... \in \mathbb{Z}$?
286
Is it true that $0.999999999\ldots=1$?
99032
Prove that the additive group of $\mathbb{Z}[x]$ is isomorphic to the group of positive rational numbers under multiplication.
71789
Prove that the sum of digits of $(999...9)^{3}$ (cube of integer with $n$ digits $9$) is $18n$
66358
Prove by mathematical induction that $2n ≤ 2^n$, for all integer $n≥1$?
12210
Show that $a^{61} \equiv a\pmod{1001}$ for every $a \in \mathbb{N}$
126015
Elementary number theory in sets
16507
Is $\mathbb{Z}= \{\dots -3, -2, -1, 0 ,1 ,2 , 3, \dots \}$ countable?
138409
Proof of infinitely many primes, clarification
65218
Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
66210
Prove that $z^n + 1/{z^n}$ is a rational number
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
6837
How to quotient $\mathbb Z [\sqrt{-11}] / (1+\sqrt{-11})$?
45460
Proof verification of a number theory problem involving sequences.
55673
Alternate proof that $\exists\ x \in \Bbb{Z}$ such that $ \gcd (a+bx,c) = 1$?
16235
Prove by induction that every positive integer is represented by some binary number?
92440
Let $n \in \mathbb{Z}^+$, prove the identity $ \sum_{k=1}^{n-1} \binom {n} {k} \frac{kn^{n-k}}{k+1}=\frac{n(n^{n}-1)}{n+1}$