初等数论证明题设n是任意正整数,α是实数,证明:[ [ nα ]/&nbs
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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,
设n是任意正整数,α是实数,证明:[ [ nα ]/ n ]= [ α ]有谁能解一下呢,
![初等数论证明题设n是任意正整数,α是实数,证明:[ [ nα ]/&nbs](/uploads/image/z/2484974-38-4.jpg?t=%E5%88%9D%E7%AD%89%E6%95%B0%E8%AE%BA%E8%AF%81%E6%98%8E%E9%A2%98%E8%AE%BEn%E6%98%AF%E4%BB%BB%E6%84%8F%E6%AD%A3%E6%95%B4%E6%95%B0%2C%CE%B1%E6%98%AF%E5%AE%9E%E6%95%B0%2C%E8%AF%81%E6%98%8E%EF%BC%9A%5B%26nbsp%3B%26nbsp%3B+%5B%26nbsp%3B%26nbsp%3Bn%CE%B1+%5D%2F%26nbs)
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}
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}