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2021 AMC 10AProblem 10P1-10~2 minPrint
Algebraic ManipulationExponents, Logarithms & RadicalsApply an identity: SFFT, sum of squares, difference of cubes, VietaCollapse a sum or product by cancellation

Which of the following is equivalent to (2+3)(22+32)(24+34)(28+38)(216+316)(232+332)(264+364)?(2+3)(2^2+3^2)(2^4+3^4)(2^8+3^8)(2^{16}+3^{16})(2^{32}+3^{32})(2^{64}+3^{64})?

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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.