Question

KƐ ŶƷŵĞƌŽƐ ƉĞƌĨĞŝƚŽƐ ĨŽƌĂŵ ŝŶƚƌŽĚƵǌŝĚŽƐ ŶĂ 'ƌĠĐŝĂ͕ ĂŶƚĞƐ ĚĞ ƌŝƐƚŽ͘ hŵ ŶƷŵĞƌŽ n Ġ ĚŝƚŽ ƉĞƌĨĞŝƚŽ ƐĞ ĞůĞ ĨŽƌŝŐƵĂůăƐŽŵĂĚŽƐƐĞƵƐĚŝǀŝƐŽƌĞƐƉŽƐŝƟǀŽƐĞƉƌſƉƌŝŽƐ͕ ŽƵƐĞũĂ͕ĚŽƐĚŝǀŝƐŽƌĞƐƉŽƐŝƟǀŽƐŵĞŶŽƌĞƐƋƵĞ nƐƐŝŵ͕͘ ƐĞ 2k − 1 Ġ ƉƌŝŵŽ͕ k > 1 ĞŶƚĆŽ Ž ŝŶƚĞŝƌŽ ƉŽƐŝƟǀŽ͕ n = 2k−1(2k − 1)ĠƵŵŶƷŵĞƌŽƉĞƌĨĞŝƚŽ͘ ŽŵďĂƐĞŶĞƐƐĂƐŝŶĨŽƌŵĂĕƁĞƐ͕ĂǀĂůŝĞĂƐĂĮƌŵĂĕƁĞƐ ĂƐĞŐƵŝƌ͘ /͘ KŶƷŵĞƌŽ 22 × 42 × 127ĠƉĞƌĨĞŝƚŽĞƚĞŵϭϳ ĚŝǀŝƐŽƌĞƐƉƌſƉƌŝŽƐ͘ //͘ KŶƷŵĞƌŽϮϴĠƵŵŶƷŵĞƌŽƉĞƌĨĞŝƚŽ͘ ///͘ Ž ƐĞ ĂĚŝĐŝŽŶĂƌ ĂƐ ƉŽƚġŶĐŝĂƐ 20, 21, 22, 23, ... ĂƚĠƋƵĞĂƐŽŵĂƐĞũĂŝŐƵĂůĂŽĚĠĐŝŵŽƉƌŝŵĞŝƌŽ ŶƷŵĞƌŽ ƉƌŝŵŽ Ğ͕ Ğŵ ƐĞŐƵŝĚĂ͕ ŵƵůƟƉůŝĐĂƌ Ă ƐŽŵĂ ŽďƟĚĂ ƉĞůŽ ƷůƟŵŽ ƚĞƌŵŽ͕ ĞŶĐŽŶƚƌĂͲƐĞ ƵŵŶƷŵĞƌŽƉĞƌĨĞŝƚŽ͘ ĐŽƌƌĞƚŽŽƋƵĞƐĞĂĮƌŵĂĞŵ

Accepted Answer

D) //Ğ///͕ĂƉĞŶĂƐ͘

Answer

A) /͕ĂƉĞŶĂƐ͘

Answer

B) //͕ĂƉĞŶĂƐ͘

Answer

C) /Ğ///͕ĂƉĞŶĂƐ͘

Answer

E) /͕//Ğ///͘

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