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A regular NT problem in Turkey TST

Source: 2024 Turkey TST P4

March 18, 2024
number theorymodular arithmeticOlympiad Number TheoryPerfect Squaresfactorial

Problem Statement

Find all positive integer pairs (a,b)(a,b) such that, 10a!−3b+12a\frac{10^{a!} - 3^b +1}{2^a} is a perfect square.
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