is divisible by 8 whenever n is an odd positive integer
1) Basic step: P(1) = 1-1 =0 is divisible by 8.
2) inductive step:
hypothesis: is divisible by 8
conclusion: is divisible by 8?
OR
is divisible by 8? <- to make it odd
help me pls
is divisible by 8 whenever n is an odd positive integer
1) Basic step: P(1) = 1-1 =0 is divisible by 8.
2) inductive step:
hypothesis: is divisible by 8
conclusion: is divisible by 8?
OR
is divisible by 8? <- to make it odd
help me pls
It is P(k+2), of course: if k is an odd positive integer, the next ODD integer is k + 2, not k + 1.
Without induction: n^2 - 1 = (n-)(n+1). As n is odd, exactly one of n-1 or n+1 is divisible by 4 and the other factor is even ==> the whole thing is divisible by 4*2 = 8.
Tonio