I need the answer as soon as possible 2. i) a) Prove that 10" =+1 (mod 11) for anynEN.b) Suppose the integer r has digits r,rn-1I, ro. Prove thatr=0(mod 11) if and only if o(-1)'r, = 0 (mod 11).c) Is 135802469132 is divisible by 11? Explain why.

Want to prove:(a) 10n≡±1 (mod 11) for any n∈N(b) If the integer x has digits xnxn-1.....x1x0 thenx≡0…

a) Prove that 10" =+1 (mod 11) for any n EN. b) Suppose the integer r has digits rI-1I, I0. Prove that r=0 (mod 11) if and only if o(-1)'r, = 0 (mod 11). c) Is 135802469132 is divisible by 11? Explain why.

a) Prove that 10" =+1 (mod 11) for any n EN. b) Suppose the integer r has digits rI-1I, I0. Prove that r=0 (mod 11) if and only if o(-1)'r, = 0 (mod 11). c) Is 135802469132 is divisible by 11? Explain why.

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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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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I need the answer as soon as possible

2. i) a) Prove that 10" =+1 (mod 11) for anynEN.
b) Suppose the integer r has digits r,rn-1I, ro. Prove thatr=0
(mod 11) if and only if o(-1)'r, = 0 (mod 11).
c) Is 135802469132 is divisible by 11? Explain why.

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