Prove that n3- n is divisible by 24 for any odd n

1.	Prove that n3- n is divisible by 24 for any odd n
Answer» Answer: Q: Prove by induction that n3−n is DIVISIBLE by 24 for all odd positive integers After proving the FIRST part for n=1 Assume TRUE for some positive integer n=k ie k3−k=24x where x is an integer Prove true for n=k+2 ie (k+2)3−(k+2)=24y where y is an integer =k3+6k2+11k+6 =24x+12k+6k2+6 But how do I get this in the form 24y? Am i supposed to use 2k+1 instead? Step-by-step explanation: PLZ mark me as brainliest

Answer»

Answer:

Q: Prove by induction that n3−n is DIVISIBLE by 24 for all odd positive integers

After proving the FIRST part for n=1

Assume TRUE for some positive integer n=k

ie k3−k=24x where x is an integer

Prove true for n=k+2

ie (k+2)3−(k+2)=24y where y is an integer

=k3+6k2+11k+6

=24x+12k+6k2+6 But how do I get this in the form 24y? Am i supposed to use 2k+1 instead?

Step-by-step explanation:

PLZ mark me as brainliest

Discussion