Let a, b, c, and d be integers, and let n be a positive integer:
101159
Prove If a ≡ b (mod n) and c ≡ d (mod n), then a + c ≡ b + d (mod n)
54699
Product of pairwise coprime integers divides $b$ if each integer divides $b$
50296
Prove $(-a+b+c)(a-b+c)(a+b-c) \leq abc$, where $a, b$ and $c$ are positive real numbers
11168
Proof of divisibility: if $a|b$ and $a|(b+c)$ then $a|c$
29971
Let $a,b,c$ positive integers such that $\left(1+\frac{1}{a}\right)\left(1+\frac{1}{b}\right)\left(1+\frac{1}{c}\right) = 3$. Find those triples.
97667
If $a<b$, $c<d$ then $a+c<b+d$?
26861
$a+b=c \times d$ and $a\times b = c + d$
51321
Prove that $A = B = C = D$
101362
Let a,b,c be positive real number, proof.
153670
Prove that if $a \mid b$ and $b \mid c$, then $a \mid c$.
981
If $n^c\in\mathbb N$ for every $n\in\mathbb N$, then $c$ is a non-negative integer?
41099
If $A \subseteq C$ and $B \subseteq D$ then $A \times B \subseteq C \times D$
135750
Prove that if a and b are integers, then there are unique integers q and r such that $a = bq + r$, $-|b|/2 < r \le |b|/2$
107173
If $a\lt{b}$ and $c\le{d}$, prove that $a+c\lt b+d$
141102
If $a,b,c$ are positive integers, with $a^2+b^2-ab=c^2$ prove that $(a-b)(b-c)\le0$.
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
46814
$ a+b+c+d=6 , a^2+b^2+c^2+d^2=12$ $\implies$ $ 36 \leq 4(a^3+b^3+c^3+d^3)-(a^4+b^4+c^4+d^4) \leq48 $