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Category > Math Posted 09 May 2017 My Price 4.00

Prove that n1, n2, n3, and n4 are pairwise relatively prime

Prove that n1, n2, n3, and n4 are pairwise relatively prime if and only if

Show more generally that n1, n2, ..., nk are pairwise relatively prime if and only if a set of [ lg k] pairs of numbers derived from the ni are relatively prime.

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Alpha Geek
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Status NEW Posted 09 May 2017 11:05 AM My Price 4.00

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file 1494328531-Answer.docx preview (110 words )
P-----------rov-----------e t-----------hat----------- n1-----------, n-----------2, -----------n3,----------- an-----------d n-----------4 a-----------re -----------pai-----------rwi-----------se -----------rel-----------ati-----------vel-----------y p-----------rim-----------e i-----------f a-----------nd -----------onl-----------y i-----------f ----------- S-----------how----------- mo-----------re -----------gen-----------era-----------lly----------- th-----------at -----------n1,----------- n2-----------, .-----------..,----------- nk----------- ar-----------e p-----------air-----------wis-----------e r-----------ela-----------tiv-----------ely----------- pr-----------ime----------- if----------- an-----------d o-----------nly----------- if----------- a -----------set----------- of----------- [ -----------lg -----------k] -----------pai-----------rs -----------of -----------num-----------ber-----------s d-----------eri-----------ved----------- fr-----------om -----------the----------- ni----------- ar-----------e r-----------ela-----------tiv-----------ely----------- pr-----------ime-----------. -----------Ans-----------wer-----------: ----------- Th-----------e i-----------nte-----------ger-----------s n-----------1, -----------n2,-----------…-----------..,-----------nk -----------are----------- ca-----------lle-----------d a-----------s p-----------air----------- wi-----------se -----------rel-----------ati-----------vel-----------y p-----------rim-----------e o-----------nly----------- if----------- th-----------e G-----------CD(-----------ni,-----------nj)----------- = -----------1 F-----------or -----------eve-----------ry -----------pos-----------sib-----------le -----------of -----------i a-----------nd -----------j w-----------ith----------- i -----------not----------- eq-----------ual-----------s t-----------o j-----------. S-----------o w-----------ith----------- th-----------e a-----------bov-----------e d-----------efi-----------nit-----------ion-----------,
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