Notes on ProjectEuler #152

這讓我想起以前數論一道題目：1 + 1/2 + 1/3 + ... + 1/n is not an integer for n > 1.

Proof: Write 1 + 1/2 + 1/3 + ... + 1/n = a/b where b = LCM(1, 2, 3, ..., n).  (a/b is not necessary reduced.)  Write b = 2^r s where r = floor(log_2(n)) and s is odd.  So a = b + b/2 + b/3 + ... + b/n is odd.  However b is even.  Therefore a/b is not an integer.



所以這題關鍵就是質因數分解。



解完這題困擾已久的題目，現在前兩百題只剩

• # 177 (Integer angled Quadrilaterals)
• # 185 (Number Mind)
• # 198 (Ambiguous Numbers)

加油。