2023 WSMO Tiebreaker Round Problems

Problem 1

Find the number of factors of $24 ^ {6} - 20 ^ {6}.$

Problem 2

If $x^3+y^3=76895, x<y$ and $x+y=65,$ find $xy.$

Problem 3

Let $S$ be the set of all values of $a$ such that the area of a triangle with side lengths $5, 7, a$ is a positive integer. Find $\sum_{x\in S}\left(x^2\right).$

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2023 WSMO Tiebreaker Round Problems

Problem 1

Problem 2

Problem 3