Abstract In this paper, we show that we can generate nonrecursive n -bit pseudorandom numbers by two times (n -bit) × \, (n -bit) multiplication and succeeding extraction of an n -bit integer from the result of multiplication. The algorithm, which we call MmS, is described using the functions defined by T 2 k (X, Y) = 2 k X Y - ⌊ 2 k X Y ⌋ + 1 T₂^{₊ (X, Y) =2^kXY- 2^kXY+1}, X, Y ∈ [ 1, 2) X, Y[1, 2), and T ˇ 2 k (X) ≡ T 2 k (X, X) T₂^{₊ (X) T₂^₊ (X, X) }. We observe and consider mathematically the condition that T 2 k (X, Y) T₂^{₊ (X, Y) } and succeeding repetition of T ˇ 2 k (X)
Hirotake Yaguchi (2026) studied this question.