Daily Archives: May 10, 2013

2013-08 Minimum of a set involving polynomials with integer coefficients

Let \( p \) be a prime number. Let \( S_p \) be the set of all positive integers \( n \) satisfying
\[
x^n – 1 = (x^p – x + 1) f(x) + p g(x)
\]
for some polynomials \( f \) and \( g \) with integer coefficients. Find all \( p \) for which \( p^p -1 \) is the minimum of \( S_p \).

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Solution: 2013-07 Maximum number of points

Consider the unit sphere in \( \mathbb{R}^n \). Find the maximum number of points on the sphere such that the (Euclidean) distance between any two of these points is larger than \( \sqrt 2 \).

The best solution was submitted by 라준현, 08학번. Congratulations!

Other solutions were submitted by 서기원(09학번, +3), 황성호(13학번, +3), 김범수(10학번, +3), 전한솔(고려대, +3), 홍혁표(13학번, +2), 어수강(서울대, +2). Thank you for your participation.

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