Prove the given statements by the indicated method. (1). By Direct Proof: "Vm, n € Z+ - {1}, m² | n² → m n."

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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4. Prove the given statements by the indicated method.
(1). By Direct Proof: “Vm, n € Z+ − {1}, m² | n² ↔ m [n.” ·
(2). By Contraposition: “V n, p, q € Z* U {0}, n+2p+3q ≥ 5 → (n ≥ 3) v (p ≥ 2) V (q ≥ 1)."
(3). By Contradiction: "V x, y, z € R, x + y, x+z, and y + z € Q → x, y, and z € Q.¹
Transcribed Image Text:4. Prove the given statements by the indicated method. (1). By Direct Proof: “Vm, n € Z+ − {1}, m² | n² ↔ m [n.” · (2). By Contraposition: “V n, p, q € Z* U {0}, n+2p+3q ≥ 5 → (n ≥ 3) v (p ≥ 2) V (q ≥ 1)." (3). By Contradiction: "V x, y, z € R, x + y, x+z, and y + z € Q → x, y, and z € Q.¹
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