The following facts are known a m and b m iff lcm ab

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Question 5.(6+4+4 points)The following facts are known:a|mandb|mifflcm(a,b)|m.()and for any2,lcm(a1,a2,...,a) = lcm(lcm(a1,a2),a3,...,a).(††)Use (), (††) and induction onto prove that for any2,ai|m,i= 1,2,...,ℓ,ifflcm(a1,a2,...,a)|m.(*)
(b) Use (a) to show thatx4(modm1),x4(modm2),andx4(modm3),iffx4(mod lcm(m1,m2,m3)).

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