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Found problems: 1

2023/2024 Tournament of Towns, 1
Tags: algebra , polymonial
For every polynomial of degree 45 with coefficients $1,2,3, \ldots, 46$ (in some order) Tom has listed all its distinct real roots. Then he increased each number in the list by 1 . What is now greater: the amount of positive numbers or the amount of negative numbers? Alexey Glebov