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Part IV (15 points). a) Write the negation, the contrapositive, the converse of the following: For a prime number

`p`

and

`kinZ^(+)`

, if 4 divides

`p-1`

, then

`p`

can be written as the sum of

`k`

squares. Negation: Contrapositive: Converse: b) State the negation of the following statements (i) For every rational number

`r`

, the number

`(1)/(r)`

is rational. (ii) There exists a rational number

`r`

such that

`r^(2)=2`

c) Prove that an integer is odd if and only if its square is odd.