JEE Main 2022 Mathematics question
Let p and p + 2 be prime numbers and let = |p!, (p + 1)!, (p + 2)!; (p + 1)!, (p + 2)!, (p + 3)!; (p + 2)!, (p + 3)!, (p + 4)!|. Then the sum of the maximum values of and , such that pᵅ and (p + 2)ᵝ divide , is .
Answer: 4
Solution
Taking p!, (p + 1)! and (p + 2)! out of the three columns, the remaining determinant has first row (1, 1, 1) and is a numerical multiple, and the printed working simplifies it to = 2·p!(p + 1)!(p +
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