x-y-N-0-1-x-y-find-z-N-with-z-x-y-

Question Number 94786 by MJS last updated on 21/May/20

x, y \in N ∖ {0, 1} \land x ⩽ y

find z \in N with z! = x! y!

Commented by hknkrc46 last updated on 21/May/20

(a) x! = y + 1 \Rightarrow z! = (y + 1)! \Rightarrow z = y + 1

(a . 1) x = 3 \Rightarrow y = 5 \Rightarrow z = 6

(a . 2) x = 4 \Rightarrow y = 23 \Rightarrow z = 24

(a . 3) x = 5 \Rightarrow y = 119 \Rightarrow z = 120

\cdot \cdot \cdot \cdot

{x, y, z : x! = y + 1 = z; x ⩾ 3}

(b) y! = x + 1 \Rightarrow z! = (x + 1)! \Rightarrow z = x + 1

(b . 1) y = 3 \Rightarrow x = 5 \Rightarrow z = 6 (x ≰ y)

(b . 2) y = 4 \Rightarrow x = 23 \Rightarrow z = 24 (x ≰ y)

\dots .