一台彩灯,3、3数余1,4、4数余2,5、5数余3,6、6数余4,7、7数余5,8、8数余6,问这台共有几个灯泡?

Question

一台彩灯,3、3数余1,4、4数余2,5、5数余3,6、6数余4,7、7数余5,8、8数余6,问这台共有几个灯泡?

Answer 1

1,4,7,10,13,16,19,22,25,28,31,34,37,40,43,46,49,---------公差3 An=3n-2
2,6,10,14,18,22,26,30,34,38,42,46,52,----------------------公差4 An=4n-2
3,8,13,18,23,28,33,38,43,48,53,58,63,68,-------------------公差5 An=5n-2
4,10,16,22,28,34,40,46,52,58,64,70--------------------------公差6,An=6n-2
5,12,19,26,33,40,47,54,61,68,---------------------------------公差7 An=7n-2
6,14,22,30,38,46,54,62,------------------------------------------公差8 An=8n-2
让这六个式子相等,求3,4,5,6,7,8,的最小公倍数6*8*5*7=1680,然后减2即1680-2=1678
所以这台共有1678个灯泡