Question

If n3 is multiple of 2, then n is divisible by 2. Prove by any method

Answer 1

Answer:

For n3 to be a multiple of 2, n = even number, hence n is divisible by 2 as all even numbers are divisible by 2.

Answer 2

Answer:

When n³ is a multiple of 2 then n is divisible by 2

Step-by-step explanation:

n³  is a multiple of 2

Let say n is not divisible by 2

then n = 2k + 1

=> n³ = (2k + 1)³

=> n³ = 8k³ + 1 + 3*4k² + 3*2k

=> n³ = 8k³ + 12k² + 6k + 1

=> n³ = 2k(4k² + 6k + 3) + 1

=> n³  is not divisible by 2

=> when n is not divisible by 2 then n³ is also not divisible by 2

now let say n is divisible by 2

then n = 2k

=> n³ = (2k)³

=> n³ = 8k³

=> n³= 2 (4k³)

Hence Divisible by 2

=> when n is divisible by 2 then n³ is also divisible by 2

=> When n³ is a multiple of 2 then n is divisible by 2