MathDB

9

Part of 2002 Iran Team Selection Test

Problems(1)

Hard number theory problem

Source: Iran 2002

4/9/2004
π(n)\pi(n) is the number of primes that are not bigger than nn. For n=2,3,4,6,8,33,…n=2,3,4,6,8,33,\dots we have π(n)∣n\pi(n)|n. Does exist infinitely many integers nn that π(n)∣n\pi(n)|n?
functioncalculusintegrationinequalitiesnumber theory unsolvednumber theory