Question

ǀĂůŝĞ ĂƐ ƐĞŐƵŝŶƚĞƐ ĂĮƌŵĂĕƁĞƐ Ă ƌĞƐƉĞŝƚŽ ĚĂƐ ĞƐƚƌƵƚƵƌĂƐĂůŐĠďƌŝĐĂƐ͘ /͘ ^Ğ I Ġ Ƶŵ ŝĚĞĂů ĚĞ Z͕ ĞŶƚĆŽ I = mZ = {ma : a ∈ Z}͕ ƉĂƌĂ ĂůŐƵŵ m ∈ Z. //͘ KĐŽŶũƵŶƚŽĚĂƐĐůĂƐƐĞƐĚĞĞƋƵŝǀĂůġŶĐŝĂŵſĚƵůŽ n͕ Zn = Z/nZ͕ƉĂƌĂ nƉƌŝŵŽ͕ŵƵŶŝĚŽĚĂƐ ŽƉĞƌĂĕƁĞƐƵƐƵĂŝƐĚĞĂĚŝĕĆŽĞŵƵůƟƉůŝĐĂĕĆŽ͕ ĠƵŵĐŽƌƉŽ͘ ///͘ K ĐŽŶũƵŶƚŽ ĚŽƐ ŶƷŵĞƌŽƐ ĐŽŵƉůĞǆŽƐ ĐŽŵ ƉĂƌƚĞƌĞĂůŶƵůĂ͕ŵƵŶŝĚŽ ĚĂŽƉĞƌĂĕĆŽƵƐƵĂůĚĞ ĂĚŝĕĆŽ͕ĨŽƌŵĂƵŵŐƌƵƉŽĂďĞůŝĂŶŽ͘ /s͘ KĐŽŶũƵŶƚŽĚĂƐŵĂƚƌŝǌĞƐƋƵĂĚƌĂĚĂƐĚĞŽƌĚĞŵ ϮĐŽŵĞŶƚƌĂĚĂƐƌĞĂŝƐ͕ŵƵŶŝĚŽĚĂƐŽƉĞƌĂĕƁĞƐ ƵƐƵĂŝƐ ĚĞ ĂĚŝĕĆŽ Ğ ŵƵůƟƉůŝĐĂĕĆŽ͕ Ġ Ƶŵ ĂŶĞů ŶĆŽĐŽŵƵƚĂƟǀŽĐŽŵƵŶŝĚĂĚĞ͘ ĐŽƌƌĞƚŽŽƋƵĞƐĞĂĮƌŵĂĞŵ

Accepted Answer

E) /͕//͕///Ğ/s͘

Answer

A) /͕ĂƉĞŶĂƐ͘

Answer

B) //͕ĂƉĞŶĂƐ͘

Answer

C) /͕///Ğ/s͕ĂƉĞŶĂƐ͘

Answer

D) //͕///Ğ/s͕ĂƉĞŶĂƐ͘

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