1.

(a) Use a direct proof to show that the product of twoodd numbers is odd.

(b) Prove that there are no solutions in integers x andy to the equation

2x² + 5y² = 14.

(c ) Prove that the square of an even number is an evennumber using

(i.) direct proof

(ii.) an indirect proof

(iii.) a proof by contradiction.

2.

Show that 1³ + 2³ +….+n³ = [n(n+1)/2]² whenever n is a positiveinteger.

3.

Determine a_n given by

a_n = a_n-1 + 6 a_{n -2} ;a₀ = 1, a₁ = 8.

Answer rating: 100% (QA)

Answer and step by step explanation 1 a Direct Proof Let two odd numbers be a and b Then a 2k1 and b 2m1 where k and m are integers The product of a a... View the full answer