# Find odd number

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2) (n+1)/2

4)

4. 2n²-3

Let n=2k

1. n² = 4k² = 2(p) where p=2k² =>even

2. (n+1)/2 = (2k+1)/2 = k+(1/2) which is a fraction

3. -2n-4 = -4k-4 = 2(q) where q=-2k-2 =>even

4. 2n²-3 = 8k²-3 = 2(r)+1 where r=4k²-2 =>odd

5. √(n²+2) = √(4k²+2) which is not an integer for any integer k

2n²-3

since 2*n² is even. (2*any integer is even). subtracting 3 from that will give you an odd number (Even – odd =odd).

option 4

4.