Question

Every even power of an odd number greater than 1 when divided by 8 leaves 1 as the remainder.The inductive step for the above statement is

• A. P(k) = (2k + 1)²ⁿ = 8a + 1 implies P(k + 1) : (2k + 3)^{2n + 2} = 8b + 1 for some natural number a,b
• B. P(k) = (2k - 1)² = 8a + 1 implies P(k + 1); (2k + 1)² = 8b + 1 for some natural numbers a,b
• C. P(k) = (2k + 1)² = 8a + 1 implies P(k + 1):(2k + 3)² = 8b + 1 for some natural numbers a,b
• D. P(1) = 3² = 8.1 + 1

Answer 1

The correct option is A

P(k) = (2k + 1)²ⁿ = 8a + 1 implies P(k + 1) : (2k + 3)^{2n + 2} = 8b + 1 for some natural number a,b