Relaxation Problems - 3

Number Theory Level 3

Let \(n\) be a positive integer and \(a, b\) be two positive integers such that \(a+b=n\). Which of the following are possible values of \(ab\) for all even positive integers \(n\)?

I. \(n+1\)

II. \(n-1\).

III. \(2n-4\)

IV. \(0.25n^{2}\)

V. \(0.25 (n^{2}-4)\)

VI. \(n^{2}\)

I, III, V, VI II, IV, V II, IV, V, VI II, IV I, II, IV, V, VI I, II, III, IV, V, VI IV, VI I, II, III, V, VI

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