Prove that n3 - n is divisible by 6 for every positive integer n.

Asked by sbhattacharya2 | 3rd Jul, 2014, 09:20: PM

Expert Answer:

 n cubed minus n space equals space n left parenthesis n squared minus 1 right parenthesis space space space space space space space space space space space equals space n left parenthesis n minus 1 right parenthesis space left parenthesis n plus 1 right parenthesis

n space o r space n minus 1 space i s space e v e n space a s space t h e y space a r e space c o n s e c u t i v e space i n t e g e r s.

P r o d u c t space o f space t h r e e space c o n s e c u t i v e space i n t e g e r s space i s space d i v i s i b l e space b y space 3. n cubed minus n space i s space d i v i s i b l e space b y space 2 space a n d space 3. H e n c e space i t space i s space d i v i s i b l e space b y space 6.

Answered by Sanjana Dhopatkar | 4th Jul, 2014, 05:27: PM