Prove that if n is an odd positive integer, then 1 ≡ n(power of 2) (mod 4).

To prove that if n is an odd positive integer, then 1 ≡ n^2 (mod 4), we can use modular arithmetic.

First, let's consider any odd positive integer n. Since n is odd, we can write it as n = 2k + 1, where k is a non-negative integer.

Now, let's compute n^2 (mod 4):

n^2 = (2k + 1)^2 = 4k^2 + 4k + 1

When we divide n^2 by 4, we get a quotient of k^2 + k and a remainder of 1. So, n^2 = 4k^2 + 4k + 1 ≡ 1 (mod 4).

Therefore, we can conclude that if n is an odd positive integer, then 1 ≡ n^2 (mod 4).

Use Mathematical Induction to prove that    1

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