MathDB

6

Part of 2010 Malaysia National Olympiad

Problems(3)

OMK 2010

Source: Malaysia National Olympiad 2010 Bongsu Category Problem 6

6/4/2011
Find the number of different pairs of positive integers (a,b)(a,b) for which a+b≤100a+b\le100 and a+1b1a+b=10\dfrac{a+\frac{1}{b}}{\frac{1}{a}+b}=10
algebra unsolvedalgebra
OMK 2010

Source: Malaysia National Olympiad 2010 Muda Category Problem 6

6/4/2011
A two-digit integer is divided by the sum of its digits. Find the largest remainder that can occur.
number theory unsolvednumber theory
Smallest integer

Source: Malaysia National Olympiad 2010 Sulung Category Problem 6

6/4/2011
Find the smallest integer k≥3k\ge3 with the property that it is possible to choose two of the number 1,2,...,k1,2,...,k in such a way that their product is equal to the sum of the remaining k−2k-2 numbers.
Diophantine equationalgebra unsolvedalgebra