2014 10B 17 · AMC 10 Step by Step

AMC 10 Step by Step

2014 AMC 10BProblem 17P16-20~4 minPrint

Divisibility & Factors Exponents, Logarithms & Radicals Modular Arithmetic 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 greatest power of $2$ that is a factor of $10^{1002} - 4^{501}$ ?

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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.