Find the remainder when 420 + 1620 + 6420 + 25620 is divided by 419 – 1
Answer
Correct Answer : c ) 340
Explanation :According to the question, we have to find the remainder in the following division:
\({40^{20}+16^{20}+64^{20}+256^{20}}\over {4^{19}-1}\)
\(=>{{4^{20}+{(4^{20})}^2+{(4^{20})^3}+{(4^{20})4}}\over {4^{19}-1}}\)
420 = 419 * 4 + 4 – 4
420 = 4(419 – 1) + 4
\(=>{{4 {(4^{19}-1)}+4}\over {4^{19}-1}}\)
⇒remainder = 4
\(=>{{4^{20}}\over {4^{19}-1}}+{{(4^{20})^2}\over {4^{19}-1}}+{{(4^{20})^3}\over {4^{19}-1}}+{{(4^{20})^4}\over {4^{19}-1}}\)
⇒Remainder = (4) + (4)2 + (4)3 + (4)4\
⇒ 4 + 16 + 64 + 256
⇒340
Hence, (c) is the correct answer.
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Originating in a particular country or region.
Native to a particular country or region.
Produced, Grown, Developed or occurring naturally in a region.
If we refer to something or someone as indigenous, it means that those things belong to the country in which they are found instead of being imported or brought from an external country.
"We went to the farm and saw many indigenous varieties of Apple."
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