题目内容
求证：3 2n+3-24n+37能被64整除.
证明：32n+3-24n+37=3×9n+1-24n+37
=3(8+1)n+1-24n+37
=3(
8n+1+
8n+…+
)-24n+37
=3×64(
·8n-1+
·8n-2+…+
)+24
-24n+40
=64×3(
8n-1+
8n-2+…+
)+64是64的倍数
故原式可被64整除.
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题目内容
求证：3 2n+3-24n+37能被64整除.
证明：32n+3-24n+37=3×9n+1-24n+37
=3(8+1)n+1-24n+37
=3(8n+1+8n+…+)-24n+37
=3×64(·8n-1+·8n-2+…+)+24-24n+40
=64×3(8n-1+8n-2+…+)+64是64的倍数
故原式可被64整除.