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Number Theory Level 3

A Sequence is obtained by deleting all perfect squares from the set of natural numbers. Find the remainder when the 200 3 r d 2003^{rd} term of the sequence is divided by 2048 2048 .


The answer is 0.

Shivam Jadhav by Shivam Jadhav , 22, India

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1 solution

Kushagra Sahni
Aug 8, 2015

Excellent question, probably one of the best I have ever solved

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If we count perfect squares less than 2100 (perfect squares are from 1 to 2025, 25 = 4 5 2 25=45^2 ) there are 45 numbers. So we have to add 23 numbers after 2025 ( 2016 , … 2016,\dots ) to get 200 3 r d 2003^{ rd} term, and we get 2048 as wanted number.

Ela Marinić-Kragić - 5 years, 8 months ago

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