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<title>组合数学</title>
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<p><span lang=EN-US style='font-size:10.0pt'>1.证任一正整数n可唯一地表成如下形式:<img width=69
height=36 id="_x0000_i1025" src="1\image002.gif" align=middle>,0≤a<sub>i</sub>≤i,i＝1,2,…。<br>
证：对n用归纳法。<o:p></o:p></span></p>
<p><span style='font-size:10.0pt'>先证可表示性：当<span lang=EN-US>n=0,1时，命题成立。<br>
假设对小于n的非负整数，命题成立。 <br>
对于n,设k!≤n＜(k+1)!,即0≤n-k!＜k·k! <br>
由假设对n-k!,命题成立，设<img width=103 height=45 id="_x0000_i1026"
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