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mn+1 \equiv 0 \pmod{24} then : m+n \equiv 0 \pmod{24} using group theory
https://math.stackexchange.com/questions/2350421/mn1-equiv-0-pmod24-then-mn-equiv-0-pmod24-using-group-theory
You're trying to prove that if mn \equiv -1 \pmod{24} then m \equiv -n \pmod{24}. Let k = -n. Then you're trying to show that if -mk \equiv -1 \pmod{24} then m \equiv k \pmod{24}. Of ...
Can we ever have \Gamma \models \perp
https://math.stackexchange.com/questions/2639449/can-we-ever-have-gamma-models-perp
That's exactly right: "\Gamma\models\perp" is equivalent to "\Gamma has no model" (or "\Gamma is unsatisfiable").
Is this proof about Mersenne numbers acceptable?
https://math.stackexchange.com/questions/86429/is-this-proof-about-mersenne-numbers-acceptable
There is nothing incorrect, but there are a few things that could be changed. We only need p>2. From 2^p \equiv 2 \pmod {p} one should conclude M_p=2^p -1\equiv 1 \pmod{p} immediately, without ...
Solving system of linear congruence equations
https://math.stackexchange.com/questions/473711/solving-system-of-linear-congruence-equations
The way you express your congruences is rather unconventional. Given that 23d\equiv1\pmod{40}, 73d\equiv1\pmod{102}, and that 40=2^3\times5 and 102=2\times3\times17, it follows that 23d\equiv1\pmod5, ...
How to prove an element of a given structure is not definable?
https://math.stackexchange.com/questions/927915/how-to-prove-an-element-of-a-given-structure-is-not-definable
HINT: If x is a definable element in a structure \mathcal M, then any automorphism of \cal M must satisfy f(x)=x. To show that 2 is not definable, find an automorphism of \cal A such that ...
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In order for \alpha\Rightarrow\beta to be valid, it must hold in all models; for \alpha\Rightarrow\beta to not be valid, there must be a model where it is false. If there is a model where it is ...
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mode(1,2,3,2,1,2,3)
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