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Difference between revisions of "1992 IMO Problems/Problem 6"

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Revision as of 00:44, 17 November 2023

Problem

For each positive integer $n$, $S(n)$ is defined to be the greatest integer such that, for every positive integer $k \le S(n)$, $n^{2}$ can be written as the sum of $k$ positive squares.

(a) Prove that $S(n) \le n^{2}-14$ for each $n \ge 4$.

(b) Find an integer $n$ such that $S(n)=n^{2}-14$.

(c) Prove that there are infinitely many integers $n$ such that $S(n)=n^{2}-14$.

Solution

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See Also

1992 IMO (Problems) • Resources
Preceded by
Problem 5 		1 • 2 • 3 • 4 • 5 • 6 Followed by
Last Question
All IMO Problems and Solutions
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