MathDB

5

Part of 2006 QEDMO 3rd

Problems(1)

Coprime to infinetely many lines of Pascal's triangle

Source: 3rd QEDMO 2006, problem 5

4/14/2006
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.
Pascal's Trianglenumber theory proposednumber theory