MathDB

4

Part of 2008 Middle European Mathematical Olympiad

Problems(2)

4n+1 and kn+1 have no common divisor

Source: MEMO 2008, Single, Problem 4

9/10/2008
Determine that all k∈Z k \in \mathbb{Z} such that ∀n \forall n the numbers 4n\plus{}1 and kn\plus{}1 have no common divisor.
number theory unsolvednumber theory
Sum of all positive divisors of n is a power of two

Source: MEMO 2008, Team, Problem 8

9/10/2008
Prove: If the sum of all positive divisors of n \in \mathbb{Z}^{\plus{}} is a power of two, then the number/amount of the divisors is a power of two.
number theory unsolvednumber theory