Question

If P(n) : n³ – n is divisible by 6, n ∈ N, then P(n) is true for all n ≥ _____________.

Answer 1

P(n) : n³ – n is divisible by 6; n ∈ N

for n = 1,
P(1) : (1)³ – 1 = 0 which is divisible by 6

for n = 2,
P(2) : (2)³ – 2
= 8 – 2 = 6 which is divisible by 6

for n = 3,
P(3) : (3)³ – 3
= 27 – 3
= 24; which is divisible by 6

Hence, P(n) is true for n ≥ 2