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Coprime to infinetely many lines of Pascal's triangle

Source: 3rd QEDMO 2006, problem 5

April 14, 2006
Pascal's Trianglenumber theory proposednumber theory

Problem Statement

Find all positive integers nn such that there are ∞\infty many lines of Pascal's triangle that have entries coprime to nn only. In other words: such that there are ∞\infty many kk with the property that the numbers (k0),(k1),(k2),...,(kk)\binom{k}{0},\binom{k}{1},\binom{k}{2},...,\binom{k}{k} are all coprime to nn.
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