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(a- c)(b-d)/(b-c)(a-d) - All-Russian MO 1996 Regional (R4) 11.6

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September 23, 2024
algebranumber theory

Problem Statement

Find all natural nn such that for some different natural a,b,ca, b, c and dd among numbers (a−c)(b−d)(b−c)(a−d),(b−c)(a−d)(a−c)(b−d),(a−b)(d−c)(a−d)(b−c),(a−c)(b−d)(a−b)(c−d),\frac{(a-c)(b-d)}{(b-c)(a-d)} , \frac{(b-c)(a-d)}{(a-c)(b-d)} , \frac{(a-b)(d-c)}{(a-d)(b-c)} , \frac{(a-c)(b-d)}{(a-b)(c-d)} , there are at least two numbers equal to nn.
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