MathDB

3

Part of 2012 Korea National Olympiad

Problems(2)

Diophantine Equation with prime numbers

Source: Korea National 2012 Problem 3

8/19/2012
Find all triples (m,p,q)(m,p,q) where m m is a positive integer and p,q p , q are primes. 2mp2+1=q5 2^m p^2 + 1 = q^5
modular arithmeticquadraticsnumber theory proposednumber theory
Maximum value in permutations

Source: Korea National 2012 Problem 7

8/19/2012
Let {a1,a2,⋯ ,a10}={1,2,⋯ ,10} \{ a_1 , a_2 , \cdots, a_{10} \} = \{ 1, 2, \cdots , 10 \} . Find the maximum value of ∑n=110(nan2−n2an) \sum_{n=1}^{10}(na_n ^2 - n^2 a_n )
inductioninequalitiesinequalities proposed