Theorem: If w, x, y, z are integers where w divides x and y divides z, then wy divides xz. Proof. Let w, x, y, z be integers such that w divides x and y divides z. Since w divides x, then x = kw and w # 0. Since y divides z, then z = jy and y#0. Plug in the expression kw for x and jy for z in the expression xz to get x2 = (kw) (jy) = (kj) (wy) Since k and j are integers, then kj is also an integer. Since w #0 and y # 0, then wy # 0. Since xz equals wy times an integer and wy #0, then wy divides xz. ■ *There is something wrong with the proof, so please do not tell me that the proof is actually correct. Thank you.

Theorem: If w, x, y, z are integers where w divides x and y divides z, then wy divides xz. Proof. Let w, x, y, z be integers such that w divides x and y divides z. Since w divides x, then x = kw and w # 0. Since y divides z, then z = jy and y#0. Plug in the expression kw for x and jy for z in the expression xz to get x2 = (kw) (jy) = (kj) (wy) Since k and j are integers, then kj is also an integer. Since w #0 and y # 0, then wy # 0. Since xz equals wy times an integer and wy #0, then wy divides xz. ■ *There is something wrong with the proof, so please do not tell me that the proof is actually correct. Thank you.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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