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The infinite sequence \(S=\{s_1,s_2,s_3,\ldots\}\) is defined by \(s_1=7\) and \(s_n=7^{s_{n-1}}\) for each integer \(n>1\). What is the remainder when \(s_{100}\) is divided by\(5\) ?

 Jan 22, 2021
 #1
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Writing out the terms and following the pattern, the remainder of s_{100} when divded by 5 is 1.

 Jan 22, 2021
 #2
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It is not 1

 Jan 22, 2021

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