1

Part of 2012 South East Mathematical Olympiad

Problems(2)

find (l,m,n) to form a geometric sequence

Source: China south east mathematical Olympiad 2012 day1 problem 1

(l, m, n)

of positive integers

(1<l<m<n)

\sum_{k=1}^{l}k, \sum_{k=l+1}^{m}k, \sum_{k=m+1}^{n}k

form a geometric sequence in order.

geometric sequencealgebra unsolvedalgebra

find six-composited numbers

Source: China south east mathematical olympiad 2012 day2 problem 5

A nonnegative integer

m

is called a “six-composited number” if

m

and the sum of its digits are both multiples of

6

. How many “six-composited numbers” that are less than

2012

modular arithmeticnumber theory unsolvednumber theory