MathDB

2

Part of 2011 Serbia National Math Olympiad

Problems(2)

phi(n,n+1) powers of two- Serbia Mathematical Olympiad 2011

Source:

4/8/2011
Let nn be an odd positive integer such that both ϕ(n)\phi(n) and ϕ(n+1)\phi (n+1) are powers of two. Prove n+1n+1 is power of two or n=5n=5.
Eulernumber theory proposednumber theory
Are there a,b,c? Serbia Math Olympiad 2011

Source:

4/8/2011
Are there positive integers a,b,ca, b, c greater than 20112011 such that: (a+b)c=...2010,2011...(a+ \sqrt{b})^c=...2010,2011...?
limitnumber theory unsolvednumber theory