Prove that 3n+2 and 5n+3 are relatively prime for every integer n.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.4: Mathematical Induction
Problem 17E
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7. Prove that 3n+2 and 5n+3 are relatively prime for every integer n.
Transcribed Image Text:7. Prove that 3n+2 and 5n+3 are relatively prime for every integer n.
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I don't understand why 3n+2 is congruent to 2n+1(modk) and 3 is congruent to 2(modk). Please explain. Thank you 

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