3楼greenjyz
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发表于 2008-11-12 10:35
只看此人
p的个位数一定是1,3,7或9。其^4的个位数为1,且p^4>10,故10|p^4-1,也即5|p^4-1;
p可表达为2k+1,则p^4-1=(2^3)k(k+1)(2k^2+2k+1),可知2^4|p^4-1;
p也可表达为3n+1或3n+2.
若3n+1: p^4-1=(3n)(3n+2)(9n^2+9n+2);
若3n+2: p^4-1=3(3n+1)(n+1)(9n^2+18n+5).
可知3|p^4-1.
因240=3*5*2^4,故240|p^4-1。.