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20 0 2年 1月号问题解答(解答由问题提供人给出 )1 3 5 1 求证 2 0 0 2 2 0 0 0 +1为合数(山东聊城三中 王章琪 2 5 2 0 0 0 )证明 因为 2 0 0 2 2 0 0 0 =(2 0 0 2 4 0 0 ) 5设ｘ=2 0 0 2 4 0 0所以 2 0 0 2 2 0 0 0 +1 =ｘ5+1=ｘ5+ｘ4 +ｘ3+ｘ2 +ｘ+1 -(ｘ4 +ｘ3+ｘ
Questions and Answers for the January 2000 issue (provided by the problem provider) 1 3 5 1 Prove that 2 0 0 2 2 0 0 0 +1 is the composite number (Shandong Liaocheng Sanzhong Wang Zhangqi 2520 000) Because 2 0 0 2 2 0 0 0 = (2 0 0 2 4 0 0) 5 sets x = 2 0 0 2 4 0 0 so 2 0 0 2 2 0 0 0 +1 = x5 + 1 = x5 + x4 + X3+x2 +x+1 -(x4 +x3+x