Question 1
SEAMO self-study edition 2027; not an official 2027 paper. Original source years are retained. 25 questions, 90 minutes; Q1–10: 3 points, Q11–20: 4 points, Q21–25: 6 points, total 100. Original response types and all subparts are preserved. Verified is an editorial convention; source defects, necessary assumptions and unresolved mathematical uncertainty are disclosed.
The sum of $n$ real numbers is zero and the sum of their pairwise products is also zero. Prove that the sum of the cubes of the numbers is zero.
The sum of $n$ real numbers is zero and the sum of their pairwise products is also zero. Prove that the sum of the cubes of the numbers is zero.