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Problem 2 vietnamese tst 2006

Source: Vietnamese TST 2006

April 17, 2006
number theory proposednumber theory

Problem Statement

Find all pair of integer numbers (n,k)(n,k) such that nn is not negative and kk is greater than 11, and satisfying that the number: A=172006n+4.172n+7.195n A=17^{2006n}+4.17^{2n}+7.19^{5n} can be represented as the product of kk consecutive positive integers.
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