Prove that the product of any
four consecutive numbers plus
1 must be a square number.
Interesting Maths Q2 (Easy)
2011-11-04 2:26 am
回答 (1)
2011-11-04 3:18 am
✔ 最佳答案
Let x be the first number ,x (x+1) (x+2) (x+3) + 1= x(x+3) (x+1)(x+2) + 1= (x² + 3x) (x² + 3x + 2) + 1= (x² + 3x + 1 - 1) (x² + 3x + 1 + 1) + 1= (x² + 3x + 1)² - 1² + 1= (x² + 3x + 1)² is a square number.
收錄日期: 2021-04-13 18:19:59
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20111103000051KK00565