Can you help me solve only (b) 3^41 - 5 is divisible by 7 Prove that (a) 340 - 4, and (b) 341 - 5 aredivisible by 7. (You cannot rely on a calculatorin your solution.)(a) 3^{40} - 4 is divisible by 7:3^{40} = (3^{2})^{20}= 9^{20} = mod 7= 2^{20} = (2^{2})^{10}= 4^{10} = (4^{2})^{5}= (16)^{5} = mod 7= 2^{5} = 32 = mode 7= 43^{40} - 4 = 4-4=03^{40} - 4 is divisibleby 70(b) 3^{41} - 5 is divisible by 7:

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Answered: Prove that (a) 340 - 4, and (b) 341 – 5…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.5: The Binomial Theorem

Problem 16E

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