Let n 1 , n 2 , n 3 , m ∈ Z and p be a prime, and write b := m + pZ and a i := 2, 3}; we denote by R the family of rainbow solutions of a 1 x 1 + a 2 x 2 + a 3 x 3 − b = 0. The first result of this paper is that if a 1 a 2 a 3 = 0+pZ and the coefficients a 1 , a 2 , a 3 are not equal, then |R| = Ω (min{|A 1 |, |A 2 |, |A 3 |}) where the constants are absolute. The second result of this paper is that if |A 1 |, |A 2 |, |A 3 | are almost equal, n 1 n 2 n 3 = 0 = m and p 0, then |R| = Ω (min{|A 1

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... , |A 2 |, |A 3 |} 2 ) where the constants depend only on n 1 , n 2 , n 3 .