Let n=63973. This is a Carmichael number, meaning it is composite but an−1≡1(modn) whenever gcd(a,n)=1. The Rabin-Miller test can be used to show n is composite by finding solutions to the equation x2−1≡0(modn) that are not \pm 1 . Use Excel to find four integers x that are solutions to this equation and are in the range 2≤x≤n−2=63971 (that is, are not ±1) Your pdf should have an explanation of what you did on your excel spreadsheet.

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