2011 10B 23 · AMC 10 Step by Step

AMC 10 Step by Step

2011 AMC 10BProblem 23P21-25~5 minPrint

Modular Arithmetic Bases & Digits Exponents, Logarithms & Radicals Apply an identity: SFFT, sum of squares, difference of cubes, Vieta Set up the equation/formula and compute; no special trick needed

What is the hundreds digit of $2011^{2011} \bmod 1000$ ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.