Is the book's proof complete for -- If $(a,b)=1,$ => $\exists s,t \in \mathbb {Z}$ s.t. $as +bt = 1$.
29692
Proof verification: elementary Number Theory Proof of $am+bn = 1$
43010
Prove that for every n ∈ Z, there exist a, b ∈ Z such that $n = 5a + 2b$.
114780
$\forall a,b,c \in \mathbb{N}\!:\ a\mid b \Rightarrow ac\mid bc. $ Divisibility Proof
138212
Please help me prove: $v(a+b)\leq v(a)+v(b)$, and $v(ab)\leq v(a)v(b)$ where $v(x)=\inf{\{\vert x^n \vert}^{1/n}: n\in\mathbb{N}\}$
89535
fake proof of $\forall a. \forall b. a = b \to 1 = 0$
94958
Prob. 6 (d), Chap. 1, in Baby Rudin, 3rd ed: How to complete this proof?
65280
If $a, b, c >0$ prove that $ [(1+a)(1+b)(1+c)]^7 > 7^7a^4b^4c^4 $.
63183
Suppose $a,b,m,n$ are natural numbers, prove that if $a({m \over n})=b$ and $(a,n)=1$, then ${m \over n} \in \mathbb{N}$
56399
Proof for $A \cup B = B$ if and only if $A \subset B$
99631
Prove/Disprove: Find $a\in S_4$ that is not a power of $b$ such that $ab=ba$ while $b=(123)$
83475
Prove Or Disprove: tr(AB)=tr(A)*tr(B)
46831
Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $
20110
How to prove $(AB)^T=B^T A^T$
130281
Proving $a^ab^b + a^bb^a \le 1$, given $a + b = 1$
139934
In $\mathbb{Z}/(n)$, does $(a) = (b)$ imply that $a$ and $b$ are associates?
134120
Prove statement with a counter-example: For all sets S, T and V, V ∪ (S ∩ T) = (V ∪ S) ∩ T is false
19046
Show that if $a$ and $b$ are positive integers with $(a,b)=1$ then $(a^n, b^n) = 1$ for all positive integers n