2020 10B 22 · AMC 10 Step by Step

AMC 10 Step by Step

2020 AMC 10BProblem 22P21-25~5 minPrint

Algebraic Manipulation Modular Arithmetic Apply an identity: SFFT, sum of squares, difference of cubes, Vieta Substitute to simplify (u = x+1/x, shifting, scaling)

What is the remainder when $2^{202} +202$ is divided by $2^{101}+2^{51}+1$ ?

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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.