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.
Suppose $a,b,c,d,e$ are consecutive positive integers with $a\lt b\lt c\lt d\lt e$. The sum $b+c+d$ is a perfect square and $a+b+c+d+e$ is a perfect cube. Find the smallest value of $c$.
Enter the exact number only; fractions are allowed.
Suppose $a,b,c,d,e$ are consecutive positive integers with $a\lt b\lt c\lt d\lt e$. The sum $b+c+d$ is a perfect square and $a+b+c+d+e$ is a perfect cube. Find the smallest value of $c$.
Enter the exact number only; fractions are allowed.