MathDB

3

Part of 2012 Thailand Mathematical Olympiad

Problems(1)

[ (m^{\phi (n)+1} + n^{\phi (m)+1} ) /mn} ] is even integer

Source: Thailand Mathematical Olympiad 2012 p3

8/17/2020
Let m,n>1m, n > 1 be coprime odd integers. Show that ⌊mϕ(n)+1+nϕ(m)+1mn⌋\big \lfloor \frac{m^{\phi (n)+1} + n^{\phi (m)+1}}{mn} \rfloor is an even integer, where ϕ\phi is Euler’s totient function.
floor functionnumber theoryEvenInteger