Prove or disprove the following statements: (a) If n E Z then the equation n3 + (n + 1)³ + (n + 2)³ = (n + 3)³ has a unique integral solution. (b) If n = a² for some a e Z then 1155 n77 + 7777n +1 (c) (n² + n+ 41)² = 1_mod 12 , for every positive integer n (d) (11 × 14" +1) is a composite integer for every positive integer n

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Prove or disprove the following statements:
(a) If n e Z then the equation n³ + (n + 1)³ + (n + 2)³ = (n + 3)³ has a unique
integral solution.
(b) If n = a² for some a E Z then 1155 n"" + 7777n + 1
(c) (n² + n+ 41)² = 1 mod 12 , for every positive integer n
%3D
(d) (11 × 14" + 1) is a composite integer for every positive integer n
Transcribed Image Text:Prove or disprove the following statements: (a) If n e Z then the equation n³ + (n + 1)³ + (n + 2)³ = (n + 3)³ has a unique integral solution. (b) If n = a² for some a E Z then 1155 n"" + 7777n + 1 (c) (n² + n+ 41)² = 1 mod 12 , for every positive integer n %3D (d) (11 × 14" + 1) is a composite integer for every positive integer n
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