MathDB

3

Part of 2007 South East Mathematical Olympiad

Problems(2)

[x] denotes the greatest integer not exceeding x

Source: China south east mathematical Olympiad 2007 problem 3

7/12/2013
Let ai=min{k+ik∣k∈N∗}a_i=min\{ k+\dfrac{i}{k}|k \in N^*\}, determine the value of Sn2=[a1]+[a2]+⋯+[an2]S_{n^2}=[a_1]+[a_2]+\cdots +[a_{n^2}], where n≥2n\ge 2 . ([x][x] denotes the greatest integer not exceeding x)
functionnumber theory unsolvednumber theory
geometric sequence

Source: China south east mathematical Olympiad 2007 problem 7

7/12/2013
Find all triples (a,b,c)(a,b,c) satisfying the following conditions: (i) a,b,ca,b,c are prime numbers, where a<b<c<100a<b<c<100. (ii) a+1,b+1,c+1a+1,b+1,c+1 form a geometric sequence.
rationumber theoryprime numbersnumber theory unsolved