Prove or disprove the following statements:(a) If n e Z then the equation n + (n + 1)³ + (n + 2)³ = (n + 3) has a uniqueintegral solution.(b) If n € Z then 24|n(3n° + 13n2 + 8).(c) If a² = b² mod m then a = ±b mod m(d) If n e Z+ then 42n + 10n = 1 mod 25.

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Prove or disprove the following statements: (a) If n e Z then the equation n+ (n + 1)3 + (n + 2) = (n + 3) has a unique integral solution. (b) If n € Z then 24|n(3n + 13n2 + 8). (c) If a? = b° mod m then a = tb mod m. (d) If n e Z+ then 42n + 10n = 1 mod 25.

Prove or disprove the following statements: (a) If n e Z then the equation n+ (n + 1)3 + (n + 2) = (n + 3) has a unique integral solution. (b) If n € Z then 24|n(3n + 13n2 + 8). (c) If a? = b° mod m then a = tb mod m. (d) If n e Z+ then 42n + 10n = 1 mod 25.

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

Prove or disprove the following statements:
(a) If n e Z then the equation n + (n + 1)³ + (n + 2)³ = (n + 3) has a unique
integral solution.
(b) If n € Z then 24|n(3n° + 13n2 + 8).
(c) If a² = b² mod m then a = ±b mod m
(d) If n e Z+ then 42n + 10n = 1 mod 25.

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