Consider: for any integers a and b, if (a3 + b3) mod 3 does not equal 0, then (a + b) mod 3 does not equal 0. (Hint: recall that a3 + b3 = (a + b)(a2 −ab + b2) (a) Give an outline for a contrapositive proof.. (b) Prove this statement.

Consider: for any integers a and b, if (a3 + b3) mod 3 does not equal 0, then (a + b) mod 3 does not equal 0. (Hint: recall that a3 + b3 = (a + b)(a2 −ab + b2) (a) Give an outline for a contrapositive proof.. (b) Prove this statement.

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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Question

Consider: for any integers a and b, if (a³ + b³) mod 3 does not equal 0, then (a + b) mod 3 does not equal 0.
(Hint: recall that a³ + b³ = (a + b)(a² −ab + b²)
(a) Give an outline for a contrapositive proof..
(b) Prove this statement.

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