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ASU 161 All Soviet Union MO 1972 4^{27}+4^{1000}+4^x, perfect square, max x

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July 3, 2019
Perfect Squarenumber theorymaximum

Problem Statement

Find the maximal xx such that the expression 427+41000+4x4^{27} + 4^{1000} + 4^x is the exact square.