题目内容
求证：32n+2-8n-9能被64整除.
证明：∵32n+2-8n-9=9n+1-8n-9=(1+8)n+1-8n-9
=
=1+(n+1)·8+
=
=
，
又
是整数，∴32n+2-8n-9能被64整除.
小结：本题关键是将32n+2写成9n+1,再将9写成8+1用二项式定理展开.
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题目内容
求证：32n+2-8n-9能被64整除.
证明：∵32n+2-8n-9=9n+1-8n-9=(1+8)n+1-8n-9
=
=1+(n+1)·8+
=
=，
又是整数，∴32n+2-8n-9能被64整除.
小结：本题关键是将32n+2写成9n+1,再将9写成8+1用二项式定理展开.