[수학과] 콜로키움 4월 11일 (A sum of squares not divisible by a prime)
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사회교육관417
A sum of squares not divisible by a prime
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제목 : A sum of squares not divisible by a prime
초록 : Let $p$ be a prime. We define $S(p)$ the smallest number $k$ such
that every positive integer is a sum of at most $k$ squares of
integers that are not divisible by $p$.
In this talk, we prove that $S(2)=10$, $S(3)=6$, $S(5)=5$, and
$S(p)=4$ for any prime $p$ greater than $5$.
In particular, it is proved that every positive integer is a sum of
at most four squares not divisible by $5$, except the unique positive
integer $79$.