Lucky number
Number Theory
Level
4
Which of the following numbers cannot divide for all integer values ?
23
11
7
3
5
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1 solution
Our expression is n²⁰⁰⁵(n²²⁰-1), if we use fermat's little theorem(p|(a^(p-1)-1) if p does not divide a) for a prime p to divide the above number, (p-1) must divide 220. This 7 is our answer since 6 does not divide 220.