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 n ≥ 2
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