I don't understand this question
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lost mantle
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I don't understand this question
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spiral junco
If $q$ is a prime dividing $1+p_1p_2...p_n$, then $q\neq p_i$ for all $1\leq i\leq n$
pure rootBOT
Omegabet_
spiral junco
@lost mantle
spiral junco
so how would i go about proving this?
show none of the p_i's divide it.
lost mantle
show none of the p_i's divide it.
would it be a fair assumption to say that i could prove this by contradiction ?
lost mantle
so i should show if q is prime diving 1 +p1..pn is q = pi
spiral junco
so i should show if q is prime diving 1 +p1..pn is q = pi
???
what
BWOC, suppose $p_i\mid (1+p_1p_2...p_n)$
pure rootBOT
Omegabet_
spiral junco
reach a contradiction.
lost mantle
i suck at prrofs
spiral junco
some integer, yes
lost mantle
kinda stuck from here
spiral junco
hint: Use 1.1
lost mantle
hint: Use 1.1
(1 + p1.. pn) = kpi?
spiral junco
that's by definition of divisibility..
lost mantle
so in order for (1+p1...pn) = q q = kpi?
lost mantle
im trying
spiral junco
nowhere did we say q=1+p_1...p_n
again, we're proving $p_i\nmid p_1...p_n+1$ for all $i$
pure rootBOT
Omegabet_
spiral junco
BWOC assume $p_i\mid p_1...p_n+1$, then there exists $k\in\mathbb{Z}$ such that $p_1...p_n+1=kp_i$
lost mantle
ok
spiral junco
now use 1.1
pure rootBOT
Omegabet_
lost mantle
now use 1.1
(p1...pn) = kpi -1
spiral junco
that is true, yes
lost mantle
am i on the right track?
spiral junco
idk, keep going and see
lost mantle
ok