初等数论证明题

题目

初等数论证明题
设n是任意正整数,α是实数,证明：[   [  nα ]/  n ]= [  α   ]有谁能解一下呢,

答案

α = [α] +{a}
nα =n[a] +n{a}
[nα] =n[a] +[n{a}]
[na]/n =[a] +[n{a}]/n
[ [nα]/n ] =[ [a] +[n{a}]/n ]
=[a] +[ [n{a}]/n ] --------n{a}