Prob 2 and prob 3 both neededPlease hundred percent efficiency neededPlease provide me correct solutionI will give your thumbs up for near and clean solution 2. Prove the following:(a) If a(b) If a3. Use congruences to prove the following:(a) 4" - 1 is divisible by 3 for every natural number n.(b) 43n+1 +23n+1+1 is divisible by 7 for every natural number n.b(modn) and c € Z then ca = cb(modn).b(modn) and c= d(modn) then a+c= b + d(modn).

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Answered: Prove the following: (a) If a (b) If a…

Math

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Prove the following: (a) If a (b) If a b(modn) and c€ Z then cacb(modn). b(modn) and e=d(modn) then a+c= b + d(modn).

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

Prob 2 and prob 3 both needed Please hundred percent efficiency needed Please provide me correct solution I will give your thumbs up for near and clean solution

2. Prove the following:
(a) If a
(b) If a
3. Use congruences to prove the following:
(a) 4" - 1 is divisible by 3 for every natural number n.
(b) 43n+1 +23n+1+1 is divisible by 7 for every natural number n.
b(modn) and c € Z then ca = cb(modn).
b(modn) and c= d(modn) then a+c= b + d(modn).

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