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(iv) Let be an odd prime number and let r be the rational number 1 r = 1+ 2 1 1 + +... 3 Prove that divides the numerator of r. (We assume that the rational number r is given in reduced form, i. e. numerator and denominator have no common factors.)

(iv) Let be an odd prime number and let r be the rational number 1 r = 1+ 2 1 1 + +... 3 Prove that divides the numerator of r. (We assume that the rational number r is given in reduced form, i. e. numerator and denominator have no common factors.)

Advanced Engineering Mathematics
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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(iv) Let p be an odd prime number and let r be the rational number 1 r =1+ 1 1 3 1 Prove that p divides the numerator of r. (We assume that the rational number r is given in reduced form, i. e. numerator and denominator have no common factors.)
Transcribed Image Text:(iv) Let p be an odd prime number and let r be the rational number 1 r =1+ 1 1 3 1 Prove that p divides the numerator of r. (We assume that the rational number r is given in reduced form, i. e. numerator and denominator have no common factors.)
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