MathDB

7

Part of 2017 South East Mathematical Olympiad

Problems(2)

CSMO Grade 10 Problem 7

Source: CSMO Grade 10 Problem 7

8/6/2017
Let mm be a given positive integer. Define ak=(2km)!3(k−1)m,k=1,2,⋯ .a_k=\frac{(2km)!}{3^{(k-1)m}},k=1,2,\cdots. Prove that there are infinite many integers and infinite many non-integers in the sequence {ak}\{a_k\}.
number theoryIntegers
CSMO Grade 11 Problem 7

Source: CSMO Grade 11 Problem 8

8/6/2017
Find the maximum value of nn, such that there exist nn pairwise distinct positive numbers x1,x2,⋯ ,xnx_1,x_2,\cdots,x_n, satisfy x12+x22+⋯+xn2=2017x_1^2+x_2^2+\cdots+x_n^2=2017
Perfect Squaresnumber theory