Divisibility problem. Prove or disprove if 𝑎|𝑏c, then 𝑎|𝑏 or 𝑎|𝑐
62770
Does $a\mid bc$ imply $a\mid b$ or $a\mid c$?
83996
For any two sets $A,B$ , $|A|\leq|B|$ or $|B|\leq|A|$
153313
Prove that for all integers $ a $ and $ b $, if $ a $ divides $ b $, then $ a^{2} $ divides $ b^{2} $.
147375
Prove :(P → Q) ∨ (Q → P) using natural deduction
75141
Quotient-Remainder Theorem Proving
113344
How do we prove that something is unprovable?
75733
Divisibility of prime numbers
61671
Discrete Math: Writing Proofs
114780
$\forall a,b,c \in \mathbb{N}\!:\ a\mid b \Rightarrow ac\mid bc. $ Divisibility Proof
91935
If $x \equiv a \pmod {p_1}$ and $x\equiv a \pmod{p_2}$, then is it true that $x\equiv a \pmod{p_1p_2} ?$
113605
In Fitch, how does one prove "(P → Q)" from the premise "(¬P ∨ Q)"?
88982
Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
85770
What is the difference between ∀x(p(x) →q(x)) and ∀x(p(x) ∧q(x))?
102757
Prove that either $m$ divides $n$ or $n$ divides $m$ given that $\operatorname{lcm}(m,n) + \operatorname{gcd}(m,n) = m + n$?
151356
Need Hints Prove "$((\neg \alpha \to \alpha) \to \alpha) $" Using Axiom 1,2,3 and MP and deduction theorem
113211
Arithmetics of cardinalities: if $|A|=|C|$ and $|B|=|D|$ then $|A\times B|=|D\times C|$
76635
Proof through combinatorial argument