If P(n) :
Question:

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

Solution:

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 ≥ 2

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